While you are informally "separated" there is not much that prevents your wife from simply leaving, however, you would still have an argument that jurisdiction lay here. I believe it is better to get ahead of the ball and PREVENT the childrens removal rather than fight the issue AFTER the fact. Whether you file formally for separation or simply initiate divorce, you will establish your jurisdiction as the court having power over the children and a standing order is entered in most juridictions precluding the disposition of assets and removing children from the jurisdiction of the Court.
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Has an action for divorce been filed? If so, there may be a standing order/restraining order issued as part of the divorce filing and this standing order has a provision that neither parent is to remove the children from the jurisdiction of the court which means that the children cannot be removed from Georgia unless you and your wife are in agreeement. If a divorce action has not been filed, you and your wife are considered the natural custodians of your children having equal rights to and for your children. It is my suggestion that you set-up a free consultation with one of the lawyers, including myself, whom provide a free legal consultation.
There is really nothing to stop her from moving with the children while you are married, with no custody (or divorce) action pending. You may still have jurisdiction to bring the custody decision back to Georgia, but why take chances? If you think she's leaving with the kids, get a lawyer, and get into court. Let me know if we can help.