Legal Question in Family Law in Georgia

As long as you are legally married you both are parents with custody and can do as you like with the children. I would advise that you seek counsel as it appears that you need to file an divorce or separate maintenance action immediately to get court intervention to ensure that your custodial rights as a father can be utilized. Once under a court order it would be unlikely that she could move without permission from the court.

Absent a court order she can carry the child (or move) anywhere in the world.

The only way to possibly prevent it would be to obtain a court order in a divorce or separate maintenance case, so you need an attorney immediately.