The fl is reborn as the demon emperor's villainess daughter from a chinese (?) novel, she meets the first ml (the protagonist of the novel, who originally was supposed to kill her) when he was a kid, and at one point of the story she almost helped him escape (i'll get to that in a minute) but he came back to return her to her room because she passed out in the rain and caught a cold.
The demon emperor was friends with the first ml's parents, but then he killed them so he can take the ml and raise him. Which is why the fl tried to help him using her wand that creates these ice crystal that are worth alot. So the ml can sell them and gain money to run away (which failed).
The fl's mother was a white haired woman that the demon emperor married for an alliance. But because the mother was abusing the fl the demon emperor cut off her hand and I think he killed her?
The second ml is a snake that turns into a kid and he's like really clingy. And I think this is where I stopped in the manhwa.
The fl is a child in all the chapters I read, and she has dark hair and somewhat pink eyes? she's really cute.
Also the demon emperor has these advisors and relatives (?) that spoil and dote on the fl and they were the ones who gifted her the ice wand.
But yeah that what I remember from the manhwa. Please help me find it