My mom claiming my kids for taxes??

Okay I’m coming here bc i want opinions. I’m 22, i have a 2.5 year old and a 2 month old. I’m back at my mothers house bc my baby dad is a cheating asshole who does nothing for our children. I’ve been on maternity leave (unpaid) so yes my mom has helped me out here and there. I owe my mom $500 bc i messed up the front bumper of her car over the summer and that’s what it costed to get fixed. And she’s also been letting me live here rent free. But i do all of the housework (i know that’s not money but gives her more time to relax and less to worry about and do when she’s not at work). She told me she’s claiming my kids this year bc i owe her. I admit i owe her and i knew it was coming from my income tax money. She told me she’ll give me some of the money but when i asked her if i could claim them and just give her money she said no she’s made her mind up and she’s not changing her mind. I was talking to my kids uncle (from dads side) and he thinks i should fight to claim them and just pay her bc they’re my kids. What do you guys think? I can see both sides. I just don’t get why if i promise to pay her why she wouldn’t let me claim them.