The children's father would not likely be able to obtain an order to stop you from moving, but could file a motion for custody of the children. In that context the court would consider is whether moving the kids is in their best interests. Moving for a better job is usually viewed favorably by a court. If the father has no visitation order and does not reliably pay support, these factors may be held against him, and it sounds unlikely that he would be awarded custody. Also, many courts have a requirement that the other spouse be notified a specified period of time before any move. Of course every case presents unique circumstances, and you should probably consult your lawyer about the specifics before making the move.
Answered on Jun 07th, 2012 at 7:15 PM