In the first book, five year old Ayla making an effort to learn the Clan sign for 'mother' so she can make it to Iza, who is at first surprised, then moved by the action.
Creb's plea to Brun to allow Ayla's "deformed" son to live, combined with Moment of Awesome. He pulls off his cloak to show the stump of his amputated arm, which he usually hides from self-consciousness, and gestures to all his scars and deformities, saying although he's seen as being a broken man (and barely even a man at all because he can't hunt), Ayla still loves and respects him unconditionally, and sees him as being "whole".
In The Valley of Horses, the moment when Ayla and Jondalar finally confess their love for each other.
In The Mammoth Hunters, Ayla starts teaching Clan signs to the half-Clan child Rydag. He approaches Nezzie, the woman who raised him, and makes a sign at her. She asks Ayla what it means and when Ayla explains Rydag called her "mother", she's reduced to tears of happiness.
A scene in The Plains of Passage where Madenia secretly watches Ayla and Jondalar make love. Normally, having a young teen girl spying on an adult couple having sex would be pretty weird or a source of Squick. However, when said teen is recovering from a vicious rape and seeing the couple together leads her to realise that what she experienced was only a perverted mockery of a genuinely loving and consensual relationship, it manages to be surprisingly moving.
In The Shelters of Stone, when Jondalar introduces Ayla to his family, they start asking questions about her past. Ayla looks to Jondalar, as she knows that they may react poorly to finding out she was raised by the Clan and has a 'child of mixed spirits'. Jondalar merely smiles encouragingly at Ayla, showing he is no longer ashamed of her past and will support and stand by her no matter what others think.