What are the chances I will be able to move out of state with my children?

I have been divorced twice and have children from both unions. My eldest is 13 and has not seen her father in almost 10 months. He has a fiancée and two children and my eldest wants nothing to do with him anymore. My two youngest have not seen or heard from their father in over 4 years. He had an FRO on him and he just disappeared during that time. Now he has suddenly reappeared just as I was making arrangements to move out of state with my family who has been my main source of help and support raising my children without a father. My parents are offering me free room and board as well as full time child care (my mother is retired) while I focus on school full time to obtain my credentials to enter the workforce with a more stable foundation. I cannot stay behind and depend on my ex spouses to help me. They have the means and flexibility to travel so visiting should not be an issue. My question is what are the chances that I have enough of a case to be granted permission to move?