All of chapter 12. Starting with Daikichi bringing up the idea of legally adopting Rin: Rin listens to Daikichi's idea of becoming "Rin Kawachi", and refuses, insisting on keeping her father's name Kaga. Daikichi is moved to tears when Rin proclaims "Daikichi, I like you just being my Daikichi." Later, Daikichi assures Rin that just because she's entering first grade doesn't mean she has to give up things like sleeping next to Daikichi or having him hold her, promising "I'll hold you even when you become an old granny, if that's what you want." Rin starts crying, but quickly breaks away from Daikichi's subsequent hug, and apologizes for not hugging him when he cried earlier and promising she'll give him a big hug next time he cries.
At the funeral when everyone is putting Chrysanthemums on her father as a final goodbye she refuses and runs off like Reina had done moments before, but she then picks two bluebells, his favourite flower, and places them on him instead.
Rin's cat-teeth grin (final photo) in the last episode gave me the wibbles because of the sheer cuteness.
The earliest, of course, is when Daikichi calls out his entire family over their callous behavior towards Rin and deciding to raise her. Unlike most instances of sudden parenthood, he wasn't under any legal obligation to care for the child, and he certainly wasn't under any family pressure to take care of her (it's strongly suggested that much of his family would have encouraged him to not take Rin in if Daikichi gave them the opportunity to object). Daikichi had a choice, and he chose Rin.
And at the end of the speech, when he asks Rin if she wants to come with him... she jumps down and runs after him without any hesitation.
While Daikichi's mother was also strongly opposed to him taking care of Rin, she jumps in and does her part immediately when she learns that he took in Rin, reasoning that if Daikichi is Rin's adopted father, then she is her grandmother. She spends much of episode 3 try to get her to open up and freaks out when she sees Rin's loose baby teeth in episode 11. She even has a picture of Rin's first day of primary school in an adorable frame next to several other pictures of Rin on top of their television.