Fiction gives us many Wedding Days. Sometimes, the couple is forced to Altar the Speed, maybe due to meddling parents or a baby on the way. The couple doesn't want to move the date up, but something or someone else is forcing them to do it. Sometimes, the couple just elopes, and avoids the big wedding mess altogether.
But every now and then, a couple ends up having TWO weddings — one for themselves, and one for everyone else. This usually takes two forms:
Elope First, Plan Later: The couple elopes, but before they can tell anyone, somebody says something to make them feel guilty for not including everyone. So they end up planning a large ceremony/reception after all. The couple will have to jump through hoops to prevent anyone from finding out they're already married. The secret may or may not be spilled, but ultimately it won't matter.
Plan First, Elope Later: In this case, the couple is planning a big wedding, but everything starts to fall apart. With all the arguments and drama, their friends and family are driving them crazy. They decide to run away after all... but only temporarily. They'll find a quick and easy way to get married (expect a very random Justice of the Peace), and then return to their big wedding to have a wonderful stress-free time, with their family being none-the-wiser. In this case, the secret will almost never be revealed.
Either way, this is almost always a Crowning Moment of Heartwarming. The couple is showing that getting married is far more important than having a big flashy wedding, and they'd rather handle things on their own terms. Arguments about flowers and who escorts whom take away from the beauty of the day, and they refuse to let that happen. But they still care very much about their friends and families to deny them their celebration. But the "real" wedding day/ceremony will always be the one the couple cherishes.
Both types are a major Truth in Television. The Trope name is a play on the title of the film My Own Private Idaho, which has absolutely nothing to do with this trope. See also Altar the Speed.
Elope First, Plan Later
Corran Horn and Mirax Terrik quietly got married in a small ceremony by Wedge Antilles, acting as captain of the Lusankya, in order to head off an outburst by Mirax's dad (since Corran's father had been the officer who sent Booster Terrik, a notorious smuggler, to prison). They later had a more traditional ceremony once it was too late for Booster to do anything.
Luke and Mara do much the same, partly on Corran's advice—they have a private Jedi wedding, and a public wedding after that.
Film - Animated
In The Princess and the Frog, Tiana and Naveen's real wedding happens in the swamp while they're frogs, but once they become human again, they have a more standard ceremony in a church.
Film - Live Action
The Wedding Banquet: Wai-tong and Wei-wei have a low-key wedding, but a chance encounter with an old friend of Wai-tong's father leads them to organize a by-the-book traditional wedding ceremony, complete with lavish banquet and dozens of guests.
Live Action Television
Niles and Daphne from Frasier. They elope in Reno, and are then guilted into not one, but two more ceremonies to make the family happy. It got really silly, and eventually the cover is blown and they fess up.
On Dharma and Greg, the title couple elope on their first date, getting married in Vegas. Naturally Greg's conservative parents are shocked, and the two wind up having a more traditional ceremony a few episodes later.
On General Hospital, Ned whisked Lois off to get married when he realized that his other girlfriend Katherine was going to blackmail him into marrying her, feeling that if he had to be a bigamist, he would at least be legally married to Lois rather than Katherine. When the shit eventually hit the fan, it took nearly a year for Ned and Lois to reconcile, but they marked their new beginning by renewing their vows with a elaborate wedding ceremony attended by all their family friends.
In Once Upon a Time, we find out that Snow White and Prince Charming actually had a private wedding officiated by Lancelot, a knight of the Round Table before the big ceremony seen in the pilot so that Charming's mother would see them marry before she died of a poisoned wound.
Manga and Anime
Paranoia Agent played with this one, but they're actually having the second service to get photographs for nostalgia purposes.
Michael and Deanna in For Better or for Worse secretly got married before they moved in together, but later had a big fancy wedding for Deanna's mother to plan.
In Abie's Irish Rose, Abie and Rose Mary ultimately have three weddings: a Methodist wedding before their feuding parents get involved, a Jewish wedding to please Abie's father, and a Catholic wedding to please Rose Mary's father.
Ethan and Lilah in Ctrl+Alt+Del run away to Jamaica, and then decide to have the big wedding after all. Hiding their already-married status until the big wedding day becomes a big plot point (and a source of blackmail for one character).
Plan First, Elope Later
In the Tales of Symphonia fanfiction Worth It, (the last in a series of eight) Zelos and Sheena find themselves facing two weddings in order to keep the peace - a huge, pretentious, overly-extravagant wedding held by the King in Meltokio and a long, boring, stuffy, traditional wedding in Mizuho. Neither wedding appeals to the couple, and as they are bound and determined to enjoy their own wedding, they grab Lloyd and Colette as witnesses and have a private ceremony at the hot springs.
In Grumpier Old Men, Gustafson's daughter and Goldman's son are planning a wedding, but it falls apart under pressure. In the end they show a wedding ceremony, which turns out to be for Goldman and Maria Ragetti. The kids reveal they eloped.
At the beginning of Fantastic Four: Rise Of The Silver Surfer, Reed and Susan have a huge wedding planned, but between the invasion of first the media and then aliens, it does not go off well. At the end of the film, they find themselves in Japan and decide on the spur of the moment that it’s as good a place as any to get married, with only their closest friends and some curious Japanese bystanders as witnesses. (Though, when Reed gets a call at the end of the ceremony—“Venice is sinking into the Adriatic!”—they still end up having to cut it off early.)
Played with in book 2 of The Hunger Games, where the characters claim to have eloped in advance of the big day, so that they can claim to have a baby on the way without, presumably, offending anyone's moral standards.
In one of The Dresden Files side stories, Billy and Georgia have their wedding, but it ultimately gets screwed up, largely in part to Georgia's (evil) stepmother, and a faerie hitman with a grudge against Billy. Legally, they were married during that ceremony, but afterwards, they have a proper (if smaller) ceremony at the local church with just them, Father Forthill, Dresden, and Murphy.
An unusual variant occurs in The Time Traveler's Wife, where the fancy wedding goes off without a hitch — except that it's the titular groom's future self, rather than his present self, who ends up standing at the altar. When his present self gets back to the present, he and his wife stop by a justice of the peace just to make sure that this version of him is officially married as well.
Played with in Patricia Briggs' River Marked: Mercy and Adam are planning a big wedding, but it's getting out of hand and all the pressure is starting to drive Mercy nuts. So they decide to have a quiet advance wedding at Mercy's church, but she wears her dress anyway since she already has it... All her family and friends are there, because Adam knew she would regret doing it without them, and they basically have the wedding they'd planned in the first place, just without the performance anxiety and scaled back a bit.
Live Action Television
Mad About You - After days of meddling family members and one disaster after another, Paul and Jamie "escape" the night before their wedding and end up getting married by a ConEd worker who also happens to be a licensed minister (played by Lyle Lovett) in a construction zone in the middle of the night. They go through with their big ceremony the next day, and the family never finds out.
In the series finale years later, after their daughter is born, they run into the minister on the street (on their anniversary no less) and discover he wasn't a real minister after all (Paul met him in a strip club during the bachelor party after all). He lied so they could have a stress-free wedding the next day. Paul and Jamie then reveal that since they thought they were married already they used silly fake names on the actual marriage certificate as a private joke (meaning they've never been legally married and their daughter was actually born out of wedlock). Hilarity ensues as they panic and try to find a way to get married that day so they can keep the same anniversary. They end up pulling this trope again.
How I Met Your Mother had an episode centered around this earlier in the same season, also with Marshall and Lily. Lily doesn't want a big wedding, feeling it would be awkward since she stood Marshall up for their first one, so the gang head off to Atlantic City for a quick wedding. Problems arise when they realise that you need a marriage license, and that it will take a couple of days. They end up going out to international waters to be wed by a ship captain, but ultimately decide to wait and have a big wedding after all.
The American version of The Office. Pam is frustrated by the way their friends are behaving at their big Niagara wedding. She and Jim run off to get married on a boat under the waterfall—which he'd prepared ahead of time, just in case this happened. Cut to them back in the church, going through with the big ceremony for their friends, and truly enjoying it because the important part was already done and now they can just relax and celebrate.
Even earlier that season, they were planning to sneak off during the day with no fanfare and just get married, but they stop by Michael's party first and realize they both actually want to go through with a big cheesy reception with all their friends and family partying and celebrating with them.
On Martin, Marin and Gena get fed up with their families and cancel the wedding in favor of a private ceremony with only Pam, Tommy, and Babyface as witnesses.
On Scrubs, Turk and Carla's planned big wedding fails to materialise when Turk gets held up in surgery and then goes to the wrong church. They still have the reception, but only get actually married at the hospital later that day when Turk goes back to check on his patient (who reveals he is a priest).
Earlier that season, they almost go through with a quickie wedding after Carla loses her mom but Turk realizes she's just having an emotional reaction and they (especially her) would end up regretting not having a real wedding ceremony with all their friends and family.
In the Grand Finale of The Latest Buzz, the stress of planning an enormous wedding (mostly to please D.J.'s mother) causes D.J. and Mr Shepherd to split up. When the kids at Teen Buzz find out, the arrange a private ceremony on the roof of the building and trick D.J. and Shepherd into turning up under false pretenses. They realise they really do love each other and go through with the ceremony.
Boston Legal: Shirley and Carl end up doing this when her priest and his rabbi nearly come to blows about how the wedding will run. They have a rather nasty fight - and then Shirley walks in, apologises, tells him that the only truly important thing is that she's marrying him, and agrees enthusiastically when he suggests eloping. They end up having a double ceremony with Alan and Denny in Nimmo Bay. Viewers pulled outhankies. They don't elope, but their wedding is much quieter than originally planned, blending the two halves of this trope.
Manga and Anime
In Wild Rock, Emba takes Yuuen away in the middle of their ceremony to make their own vows of eternity alone.
In Rocko's Modern Life, when Filburt and Dr. Hutchison get married, they have a big, traditional wedding planned. But because their families (cats and turtles) don't get along, and because Dr. Hutchison's mother was too involved, the couple have a Drive-Thru wedding before appearing at the park where the ceremony was to be held.
On Gilmore Girls Lane and Zach's weddings put an interesting twist on this pattern. The first wedding is a Buddhist wedding to satisfy Lane's grandmother from Korea, the second wedding is a proper Seventh Day Adventist wedding for Lane's mother and extended family in America, and then the reception is done in a style more appropriate to the couple themselves.
In Papa Married a Mormon, precursor to The Great Brain books, Tom,Sr. and Tena marry four times. Tom whisks Tena away to Salt Lake City, where they get married by a justice of the peace a few days before her eighteenth birthday. When she turns eighteen, they go back and marry again. Shortly before the birth of their first child, the bishop agrees to marry them in a private Mormon ceremony and even fudges the date so no one will say anything about the child. Years later, they have small Catholic ceremony when Tom, Sr is on his deathbed.
Will Riker and Deanna Troi in Star Trek: Nemesis have a Starfleet wedding in dress uniform on the Enterprise, and then a Betazoid ceremony for Lwaxanna's benefit. We don't get to see that one.
In Night Court, Bull Shannon - noting that most of his friends and family are at each other's throats regarding the plans for his upcoming wedding - winds up improvising a ceremony on the courthouse roof while insuring that everyone's complaints get addressed.
He stops the fight between his fiancee Wanda and his mother over Wanda's refusal to wear a family heirloom wedding dress by having the dress tailored into a formal jacket for himself.
He stops the fight between Harry and Art over who will be the Best Man by asking Harry to perform the ceremony, having Art give the bride away and choosing Roz as his Best Woman.
This can be invoked in The Sims, if the player chooses "Have Private Wedding".
Inverted in The Secret Agreement, where Iori conducts his own private "I don't" when he only pretends to drink from the marriage cup that is part of his Arranged Marriage ceremony. His sister, who is under the illusion that he just doesn't like taking food from people who aren't her or their mother, notices it and laughs about it privately with Yuuichi, who recognizes it for what it is—Iori symbolically indicating that even if he's married, his love is only pledged to Yuuichi.
In the novel Breach of Promise by Perri O'Shaughnessy, Mike and Lindy Markey are revealed to have had their own private "I do," at a small church in Mexico. However, unlike most examples of this trope, they never do get around to having a "real" wedding, and their ceremony in Mexico has no legal force. This causes some serious problems for Lindy, when Mike has an affair with a younger woman and wants to kick her out of his life... They eventually do get back together and get married legally.
Shane and Mara from The Shield run away to get married, probably because they didn't had anyone to invite anyway.
In My Wife and Kids Junior and Vanessa marry in Las Vegas to escape from a over-the-top marriage.
Tomoya and Nagisa elope in CLANNAD ~After Story~ because they're too poor to afford a "proper" wedding.