Easily overlooked, but the other girls (except Mertle) are nicer to Lilo than they were in the first movie, speaking to her politely even when she interrupts Kumu's announcement, letting her join the circle when they're talking about ideas for the hula competition and talking about how her mother was cool. One of them even rebukes Mertle gently when she insensitively points out that Lilo's mother is dead.
There's a scene where Lilo is frustrated about her missing parents and what's going on in her life right now, and Nani, as always is trying her hardest to reach her. They fight a little, but in the end they connect over their memories over their mother, and Nani reassures her that her mother will always love her.
Nani: Maybe I don't know everything, but I'm sure Mom would be proud of you just for being you. Lilo:(mid-hug) You too. (Nani's eyes shoot open, and she looks shocked at the very idea.) Nani:(extremely touched) Thanks, Lilo.
Especially heartwarming given that the scene began with Lilo saying in a fit of anger that Nani's best would never measure up to their mother. Given her Promotion to Parent making that portrayal rare, it really works when the series points out that Nani's also a daughter who lost her parents, and isn't sure what to do - especially since she's usually the Chew Toy.
Jumba and Pleakley trying to help when Kumu comes over the house. Things go horribly wrong and they weird Kumu out, but the fact that they tried to defuse the situation and make Lilo seem like a precious angel is touching.
The end, where it seems that Stitch has died...only for Lilo to save him. This exchange between Jumba and Pleakley sums it up perfectly:
Pleakley:(astonished) But how is this possible? Jumba:(overjoyed)It's not!
When Jumba's fusion device breaks, he reveals he bought the original one and is downhearted when it fails. Pleakley gives him some reassurance about his intellect and that he could save Stitch. He looks to the screen...and says this:
The flashback to Stitch's creation is both this, a funny moment and a bit of a Tear Jerker at the end—after Jumba creates Stitch, he initially expresses horror at how adorable he is...only to be relieved when Stitch reveals that he's also vicious. Jumba spends the rest of the scene speaking to and about Stitch like a proud father, plugging in the machine to charge up his molecules and telling him he has a surprise for him (and expressing pride when the little guy immediately starts trying to get a peek at said surprise), which turns out to be his space suit from the original film. When Jumba's arrested and the machine charging Stitch's molecules is unplugged, Jumba's more concerned for Stitch than himself, crying out "What will become of my little monstrosity!?" as he's dragged away from him and his machine is destroyed. Even before Jumba and Stitch had their official redemption, it's clear that they cared for each other.
Stitch holds Lilo back from fighting Mertle... until Mertle insults Lilo's dead mother. Then, like a good friend, he lets Lilo beat the ever loving snot out of Mertle.
The Origin of Stitch
This short film is just one big heartwarmer, particularly when Jumba hugs Stitch just like a father would.Aww...