Just from what you outlined in your post, I immediately see that you have a lot on the ball. The problem seems to be your mom's and not yours, small consolation I know.

I think you should let your dad know that you are thinking of leaving home. I know that he will not want you to do this, and it could lead to him getting your mom help, which she is in desperate need of in my opinion.

I think that you should stay home at least until you try this proactive option. If you could stay until you graduate from high school, and you choose to go to college, this would give you the separation you desire. And if your mom is able to work out her problems, maybe the entire situation could be corrected and your home return to normal.

It sounds like your mom has mental health issues that are creating this toxic environment in your home. This can be remedied if she is able to admit that she needs help.

Good luck to you.