Heartwarming / Avatar: The Last Airbender The Search
This exchange between Zuko and Sokka.
Zuko: After all those snowballs to the head, you still look out for her.
Sokka: I throw witticisms at her, she throws snowballs at me, the relationship works.
Zuko: Seems to me you're getting the short end of the deal.
Sokka: (glancing at a sleeping Katara with a smile) Katara is my sister. When it comes to her, I don't mind getting the short end of the deal.
Which leads to Zuko trying to reach out to Azula in a similar manner. Despite everything, he truly does want him and Azula to be a family again.
Before going to see Zuko, following her banishment, Ursa stops by Azula's room and gives her a kiss goodbye while she sleeps.
Early on in Part 2, Azula gets the belief in her head that Zuko must actually be on "her side" and not under their mother's "control". Because of this, she spends the whole book trying as best as she can to work with him and even try to reconnect as siblings. Sadly, it's (sort of) back to square one at the end of the book...though it does end with a Hope Spot.
It may also count as a Funny Moment, but seeing Aang and Katara kiss during the Big Damn Kiss between the actors at the end of Love Amongst The Dragons...that's really nice.
Whenever Azula sees an illusion(?) of her mother, Ursa is always saying how much she loves Azula and begs her to leave the self-destructive path she is on.
Reaches new heights when she finally finds her mother. Ursa, as Noriko, met Azula who went on a Motive Rant, all Noriko could do is apologize to Azula for not loving her enough, and then doesn't hesitate to accept the Mother of Faces offer to return her memories, even knowing they would be bad, for her children.
While sitting with Noren, Kiyi and Noriko, whom Zuko now knows is actually his mother Ursa. Zuko asks Noriko if she is happy with her life. When Noriko happily answers that she is, Zuko smiles and makes to leave without telling Noriko the truth of her identity.
The final confrontation with Azula. Azula, fully defeated, asks Zuko why he didn't just kill her when he had the chance on the cliff unless he just wanted to use her to get the peaceful life he always wanted. Zuko replies that he always knew deep down that he could never have that life...the real reason he didn't kill Azula? Because even though their relationship is strained and may never recover, she's still his sister and he loves her. This is so affecting that it actually prompts something of a HeelFace Turn from Azula.
When the Mother of Faces appears to them and offers Noriko the chance to have her memories of being Ursa back. Zuko pleads with her not to go through with it. Arguing that she doesn't need to give up the beautiful life she has as Noriko.
Zuko's reunion with his mother is far from as joyful a one he and most of the fanbase hoped for, and there is a lot of pain and regret on both sides. However, both Zuko and Ursa are dedicated to rebuilding their relationship and the story bookends with Zuko asking his mother to tell him all about the story of her life. It helps put the sweet in this Bittersweet Ending.
Ursa: "I may not have the right to be, but I'm proud of you too."
For Koh, no less. He just misses his mother...
Zuko's moments with Kiyi are downright adorable. Even more so once it's revealed that Kiyi is actually Zuko's half-sister.
During their second meeting Kiyi rushes to give Zuko a big hug.
Kiyi: You came back! You came back because we're best friends!