Document everything.
You didn't say how the kids feel about the move. If they don't want to move and say they want to stay with mom could be a problem. In our case the GAL determined my SD was "mature for her age" and took her wishes (which were very tainted by coaching from her mother's family)highly into consideration.
Even then it seems it would be difficult for mom in this situation. Could waste a whole bunch of your money though.