Emphasis on "Moment": When listing off his excuses for not joining Silas Ramsbottom, the first one Gru says is "I'm a father now." It further emphasises the point of the entire first movie... it's not a real Heel-Face Turn. Gru didn't become a hero, he became a father which can be much, much more than a mere hero.
The scene with Agnes at the beginning, especially the last line:
Gru: Good night, Agnes. (Kisses her forehead) Never get older.
Gru & Lucy's and Margo & Antonio's relationships are extremely adorable.
After seeing Margo heartbroken because of finding out that Antonio is a Kid A Nova, Gru freezes him with his freeze ray. It's funny and it would remind one of a parent comforting you when you get your heart broken. Gru just did what any father would do in his position (Note: Yes, Gru's "position" always includes "...and I have a Freeze Ray").
Agnes finally being able to recite her poem at Gru and Lucy's wedding, and adding "And my new mom Lucy is beyond compare." Then she tackles her with a hug.
And Gru realizing what Agnes is trying to say, smiles, and encouragingly tells her in the most gentlest voice: "Okay." Father of the Year goes to Mr. Felonious Gru.
The look on Lucy's face when Agnes recites the poem is just perfect. She looks like she's about to cry. And her little "AWW!" at Agnes's poem is just so sweet!
Two seconds later Margo and Edith join in with Agnes. The latter gets picked up by her father and the former hugs her mother's legs, while her mother hugs her with one arm (the other arm still supporting Agnes). This family is just precious!!!
Dr. Nefario's reason for saving Gru from the mutant minions.
Dr. Nefario:I mean, I'm happy to create an evil army and destroy the world. But nobody messes with my family.
Gru dresses up as a fairy princess at Agnes' birthday part when the woman he hired had to cancel.
It gets even better when Agnes whispers at him that she knows it's him and not a fairy princess, but she's still very glad for him doing it. Seriously, Gru's later expression speaks volumes of how much he loves the little girl.
There's something really sweet about this exchange between Gru and Lucy as they're preparing to jump off the rocket and into the ocean.
Gru:Lucy, we may not get out of this alive. So, I need to ask you a question.
Lucy:Uh, better make it quick!
Gru:If I asked you out on a date, what would you have said?
Lucy:*laughs and smiles* Uh, are you kidding me? Yes!
Even more heartwarming? After Lucy tackle-hugs Gru, she immediately gives him his space, probably remembering the cupcake incident and its aftermaths. But without one word, Gru firmly grabs her hand and pulls her back into his personal space. In the most romantic gesture imaginable, Gru silently tells Lucy he wants her to never leave his side again. These two are the cutest.
Gru and Lucy kissing at their wedding. They bump noses the first few attempts before Lucy plants one on him.
Lucy's goodnight kiss to Gru after she helps him take Shannon home, especially the look on Gru's face afterwards.
For the record, Gru's smile is absolutely adorable!!
After Dr. Nefario saves the girls from a mutated!Kevin, all the girls look relieved and happy to see him. Agnes even said his name to express their happiness of seeing him back to normal. Now remember that there are thousands of minions who might resemble Kevin and the girls might have forgotten his name or mistook him for another minion. But they didn't because in the year that they've been with the minion, they actually get his name right. It's a subtle way of showing that like their father, the girls have possibly learned all the names of the minions!
Not to mention before that. When the girls are cowering from Mutated!Kevin, Edith steps forward and positions herself to fight him and protect her sisters.
The girls coming to visit Gru at work. Then, after Lucy causes an awkward moment ("Are you single?"), the girls are given some money and are "encouraged" to visit the mall by their father. The girls say goodbye and leave, but then run back and give their dad a tackle hug and tell him good luck on saving the world. Just another way of showing how much these girls adore their father!
Just look how concerned the two minions are when Gru is being kidnapped by Lucy.
This may be easily missed, but at the beginning of the film, when the girls are being put to bed, you can see Gru had transformed Agnes' bomb bed to look like a unicorn bed.
At the ending, during Gru and Lucy's wedding, Silas (Lucy's boss) can be seen in the background with Natalie. Don't remember? She's Jillian' s friends that she tried to hook up with Gru at Agnes' birthday, earlier in the film. Then, both Silas and Natalie are dancing when the Minions sing their version of "YMCA". And their both having a great time together! We can see Silas with a real smile on his face and he's not being smug; Natalie is with a guy she really likes. For some reason, seeing those two together is just so sweet and adorable.
It may be hard to notice, but if you pay close attention to the Minion with the glass jar on his head throughout the film? Well, he's also also constantly with another Minion. And they're a couple!
Lucy and Gru inviting Silas to their wedding. It's clear that they probably don't like him, but maybe it implies that during the Time Skip the couple grew closer to Silas.
They also invited Shannon to the wedding as well, probably to show that they have no ill will towards her.
Lucy first meeting Margo, Edith, and Agnes. She kneels down a little with a big smile on her face and when Gru introduces each of them, her eyes briefly lock on to each. Then, she even does a cute "nose wiggle" to little Agnes.
Then when the girls leave, Agnes waves goodbye to Lucy. And what does Lucy do? She waves back.
When the rocket reaches inside the volcano, you can briefly see Gru with his arms around Lucy while their falling to the sea; one holding her hand and the other around her shoulders. He's doing what he wanted to do, but couldn't when Lucy was reassigned to Australia: Keep her close to him.
Fridge Brilliance: It's hard to notice but Lucy's wedding dress has two ruffle patterns. Now look at Agnes' dress... it has two ruffle patterns as well. In other words, Agnes was matching up with her mother.
A small and brief one, but Edith playing with Kyle, and the latter having Gru's unopened wig in his mouth.
Agnes telling everybody "I'd like to make some toast" is simply adorable.
Also this one: "To the bride and Gru!"
Another small one, but just the way Gru delivers this line to Lucy: "Don't worry. I will get you out of this."
At the birthday party at the beginning of the movie, Agnes (whose party it is) is wearing a dress which has been carefully tailored to make her look like she's riding a unicorn. Probably also counts as Awesome.
Gru carrying a sleeping Agnes to her bed. Also even more adorable is Agnes is resting her head on Gru's shoulder.
This lyric from the ending theme is just really nice:
"Cause I can show you how to make your worst day feel like your birthday."
Lucy tranquilizing Shannon after she'd spent the night tormenting Gru. It's reminiscent of the first movie, when Gru shoots the arcade after the booth's manager started tormenting Agnes. Shooting the Jerkass Victim = family.
Right before Lucy kisses Gru on the cheek
Lucy: Oh, just between you and me, you look much better bald.