If I am moving to another state without my children's fathers, how do I prevent legal action against myself?

I am looking for advice on what I need to do legally, so that I may move to another state with my children. I have 6 and 3 year old. They both have two different birth fathers. Now, my daughter, who will be 7 in May. Her father was not supportive at all with her. I don’t see a penny from him for her. When she was a baby, he gave me money in money orders. I believe that stopped around her being 8 months. He hasn't seen her since her birthday in 2013. He's requested to see her but never follows through. I’ll try to contact him when her wants to come pick her up. He doesn’t reply. She is a Tohono O'Odham Native American and Mexican American. Born in Tucson Az. She does NOT receive any help from her tribute either. She does have a TO number but doesn’t receive help. Also, up until recently. Her father lived with his mother on the reservation. I couldn’t get child support or state help for her, because the state has no jurisdiction. Now that he's moved off the land. I have to try and get child support for her. Now my son, who just turned 3 in march, his father is in his life. By court order there is child support order on his father. He does also visit with his son every other weekend. Although he "visits" with his son. Elijah, our son, would majority of the time would be with his dads girlfriend at the time being. My son would always come home talking about his, "ju ju". Which is his dads girlfriend. Now that they are no longer together, his father has asked me questions daily as to how to take care of his son. He has to ask me what he likes to eat, how his habits are, and what to do when his bad. Also, when he was bad a few times he would try to bring him back to my place. Now I have no problem with him asking these questions. My thing is, is that our son is 3. His been visiting with him since he was born, but he has no idea how to handle his son. I never held my children from their fathers ever.