Please understand that not paying child support has really nothing to do with the right to see your kids. In other words, you can not withhold visitation becuase he is not paying support.  It sounds kookey but it is the truth. And you should consider suing him for the back support and obtaining a judgement.  But that is not really the issue here.  You want to move.  If you have a custody provision that permits visitation and restricts moving and he agrees to modify and allow you to move then do an Addendum to the stipulation.  If you can not get him to agree then yes, make an application by motion to the Judge to allow you to move. Better life, Fiance supports them, etc.  Good luck.