W.P.
This is a complex question and I understand you are feeling exhausted by the situation. However, I fear you will always regret it if you move out of state. Your children may well feel abandoned by you because you really will be much less able to connect with them. You don't go into the details of why it is such a battle. What about shared custody or something like that? I don't see why he should have total custody of them in there are no other issues except that he has them now. Do you have a decent lawyer/advocate for yourself? Also I have to stress-it isn't up to the child. Children don't make those kind of major life decisions for themselves when they are 9 years old. I'm sure she is totally torn like most kids are when this happens and very confused. I wouldn't let her "attitude" toward you influence your decision. Plus who knows what her father is saying about you etc.
Yes, you have to balance what is best for you and what is best for your child. I think most courts agree that it is very important for the mom to be a part of the life of the child. If you have to move for your job that is indeed very tricky. I doubt your daughter will want that, given the circumstances. Your husband should be willing to share custody with you and it doesn't sound like he is. He is not putting the best interest of your child first. I would be trying to work it out with him somehow and not just battle. Is that possible? What about having a court appointed advocate for your daughter? It is their job to determine what would be best for the child.
I wish you the best of luck. I would consult a therapist for yourself right now. This is a major life desicion and should be made with some expert help, someone you trust. etc. I don't think you should do this under duress but from a calm state of mind. Let us know what happens.