AITA for sending my daughter to live with her mom because of what she said?

4 days ago my daughter(14) and I got into a fight, basically she was rude to her teacher and refused to apologize because “that bitch deserved it”. We got into a fight over this and she yelled that she hates me and wishes I was dead.

I tols her to get into the car and took her to her mom’s home. She apolgized and asked me to let her stay with me but I said no this is how your life is going to be if I’m dead. You have to exprience it and left her there.

These past 4 days she has been sending texts begging me to let her come home but I haven’t answered any of her texts. My mom found out about it and called me a heartless asshole. Am I?

I must add that her mom is the every other weekend parent. She is not abusive or anything like that she is just very cold and my daughter hates her for that