This is the right answer. In most places that I'm aware of, HS ball is optional. If your DD wants to play at the next level, not playing in HS won't really matter. So the coach doesn't really have the authority that he is trying to abuse. I wouldn't be too worried about the HS coaches wishes, and just do what is best for her.Forgot about the animosity. That is irrelevant.
1) what does your DD want to do?
2) does the other team provide a better opportunity that is feasible for you as a family.