"I would very much like to put my arms around you, unless the embarrassment would kill you." Oh Malfoy...
Violet's simple response of "I think I'd live" along with the fact that Malfoy does embrace her makes this moment even more heartwarming.
The boys all inviting Violet to their houses for Christmas and her reaction.
Another one for Violet: After getting to spend Christmas Eve with her father and baby brother, and Teddy asks her if she had a good time, she drops her guard just for one moment:
"Scorpius is talking now. He calls me 'Vi-Vi'."
When Chloe adjusts a tied up Aisha's headscarf to cover her hair. It's a small, but touching moment that shows how much Chloe's changed over the course of the story. It's worth mentioning that keeping her hair covered may well be a part of Aisha's religion, which makes this moment even more touching.
The Hogwarts staff create an obelisk as a reminder of everyone who helped protect Hogwarts from the Goblin attack. Various students names are added to the plaques, then one by one, more suggestions are made. Chloe Grey is added, along with the deceased Alduin Dolohov. Then the names of all of the house elves who helped are added too, much to their own surprise.