Lots of stuff here, assuming you are a minor because if not you should move out immediately.
First about the AC, I would recommend you ask to turn it on when the temperature is at a certain level in your room, say 80 or whatever your parents can agree to which is a more reasonable way to control it.
Next, I think daring your father to disown you sounds like a bad idea, I would not recommend you to escalate the situation since it sounds like a very poor relationship. If your mom can’t help, maybe you have grandparents that can help you? Good luck, try to hang in there.
Path of exile