I have four kids with my ex, 1 adult child, 2 teenagers and a 9 year old. I'm losing my home as a direct result of my ex's alcoholism and lack in paying child support. He moved 50 miles away from us and doesn't see the kids even though he says I'm keeping them from him (yes, I'm keeping my teenagers under lock and key, ha) We have no family here and since I'm losing the house anyway, I'd like us all to move to another state where we at least have family and some support system. Can he really even have a say or a good fight in keeping us from moving in this particular case?

Yes! It all depends on what the court has ordered in terms of custody and visitation. If there is any court ordered visitation, then you have to go to court for a modification of the order. Otherwise you can get in trouble for defying the order.

If, the facts are as you state, then a court should allow the move.