This story is an aftermath of "A Canterlot Wedding," it goes into bigger detail on what Princess Celestia, Shining Armor, and the Mane Five are all quite surprised that Twilight Sparkle shows no resentment for leaving or shunning her. Even though they've shown regret for it, Twilight Sparkle insists not to be so hard on themselves, and that their actions are understandable.
Until later on... She admits that she felt resentful towards them for abandoning her but her friends assured they were going to talk to her after the reception, and never really going to abandon her.
Equally heartwarming are the lines that immediately follow. Applejack says that Twilight made them all worthwhile, a point which Twilight shoots down without missing a beat. What makes it heartwarming is what she follows up with:
Twilight Sparkle: Everything that I've ever done worth bragging about is because I've had one of you at my side, keeping me strong. It isn't me that makes all of you worthwhile...it's the other way around. I don't want you to ever forget that.
This gem during Luna and Celestia's conversation after the wedding.
Celestia: You know, I've always envied Twilight's parents. Because no matter how much Twilight might love me, adore me, and strive for my approval, they will always hold the place in her heart that I want.
Luna: You love her that much?
Celestia: Like a daughter.
Twilight's reaction to finding out that Spike wants her to be his mother. After initially being stunned, she's deeply touched by the idea.
The entire sequence between Twilight and Spike in the "Lullaby" chapter. Words do not do it justice.
When one of Olive Branch's co-conspirators comes to Ponyville to defame Spike for drawing a gang of dragons near town as part of some tyrannical plot of Princess Celestia's, how do the citizens respond? By running the conspirator out of town for picking on one of their own and insulting their princess. Even the Keeper compliments the townsponies for their valor.
What makes it truly heartwarming is who the first pony is to interrupt the conspirator: Bon Bon, the one pony whom Fanon has painted as the most critical of the Mane 6's (and Lyra's) usual shenanigans.
While Pinkie's history with her actual parents fall under Tear Jerker, her history with the Cakes is pure this. Mrs. Cake first met her as a hungry foal and offered her some baked goods. Pinkie decided to help and ended up spending the night. She never left and the Cakes basically became her parents.
Mrs. Cake: You know we've never regretted taking you in, right?
Pinkie: I know. I've never regretted coming here.
The Tear Jerker quality of Pinkie's family history is what makes her reunion and reconciliation with them all the sweeter.
Rainbow Dash letting Scootaloo sleep at her house after her parents are arrested.
Soarin' telling Rainbow Dash that he'll help her take care of Scootaloo when she adopts her.
It's a milder example, but it's touching that Owlocious has taken on a mentorship role for Peewee.
Rarity dropping everything, even her part in the investigation, to care for Sweetie Belle when she gets sick.
The exchanges between Rainbow Dash and Scootaloo showing that the latter is Happily Adopted.