My question involves a child custody case from the State of: MA

I have Sole legal and physical custody of my 3 children due to my ex being a drug addict. He has not seen his children in 4 years and has never paid child support. I have recently gotten remarried and the children on their own have started to call my new husband "dad" and have legally taken my new husbands last name. Now my ex has finally got a job after getting out of prison and wants to pay child support and get visitation. My current husband has military orders to move, can my ex prevent us from moving ? Can he even get visitation? And if so, how long does it usually take through the courts for it to go through?