I am a GA attorney, just so you know.
Realistically, there is not enough time for you to apply to the court to do anything during this visit.
As DYFS didn't find reason to remove the children from your ex, then an emergency custody order is not likely to be approved. And a formal petition for Modification of Visitation would not be heard until weeks after the 5 week visit has ended.
For the time being, all the children can do is lay low and wait for the visitation to end.
A change of jurisdiction for child custody is very difficult to get unless both parents and all the children are no longer residing in the state that issued the original custody order. While the law is complicated, I will try to explain it to you, so you can understand the laws at work here.
It is not state law, but rather federal law---through the Uniform Child Custody Jurisdiction and Enforcement Act (UCCJEA)---which determines what state has the right to make a Child Custody award, or a Modification of a Custody award.
It is important to understand that Under the UCCJEA, A court in one state that initially issues a custody order has what is known as exclusive continuing jurisdiction, and continues to have the right to modify that order until one of two things happens:
1. The original court loses what is known as significant connection jurisdiction, or
2. Both parents and the child have moved from the state which issued the original custody order.
As for item 1, it is for the court in the original state to make the determination whether they have lost the significant connection jurisdiction. Any state may make the determination that the child and both parents have left a state.
So long as the original state has exclusive continuing jurisdiction, no other state may modify the custody order.
So, when just one parent and their child relocate to a new state, and the other parent remains in the state with significant connection jurisdiction, the new state the child lives in can only modify the custody order if the old state agrees that it has lost significant connection jurisdiction. This is done by a parent showing the court with continuing jurisdiction that the new state can best protect the parties---if there has been domestic violence or abuse against the child---or by showing that the child has resided in the new state so long that most of the evidence necessary to proving the best interests of the child are located in that new state, and therefore, to continue the jurisdiction in the old state would create an inconvenient forum for the parties.
Finally, if a parent takes their child to another state to escape domestic violence, or to protect the child from the physical abuse of the other parent, an inquiry must be made into whether the flight from the first state was justified, and if it was, the original court may decline jurisdiction and allow the new state to exercise jurisdiction.
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I wish you the best in 2013,