In 1978, the NC Court of Appeals held that a parent cannot kidnap a child from the other parent, unless there is a court custody order providing that the other parent is entitled to custody of the child. See, North Carolina v. Walker, 35 N.C. App. 182, 241 S.E.2d 89 (N.C.App. 02/07/1978). Since that decision, the NC Kidnapping laws have been modified by the state legislature in a manner which suggests that it could be possible to kidnap a parent under conditions that were present in the original Court of Appeals decision. See NCGS 14-41. However, there is no reported case of a parent actually being charged with kidnapping under the circumstances you describe, so from all available information, there is nothing to prevent you from leaving for GA with the children.
Upon discovering that you have left the state, the father can petition the family court for custody, and if he receives a temporary sole custody
order, he may be able to force you to return the children to NC -- though you could not be criminally charged for kidnapping. If you want to prevent this from occurring, then as soon as you reach GA you would have to file a petition for a temporary protective/restraining order
against the father alleging abuse and if the court agrees and orders the restraining order, then the NC court could not force the children's return, unless and until the GA court decides to terminate the temporary order
The point is that there is a risk, but it may not be as great a risk as the risk of staying in NC. That's something only you can decide.
Your other option would be to seek a restraining order in NC family court alleging abuse which would force the father to leave the family home. Then you could petition for custody orders yourself, and as part of those orders, you could obtain orders to move to GA.
I understand your circumstances, and frankly under the circumstances, I cannot definitively say which route is better. But, at least now you know what the law is and is not, and so you can decide for yourself.
Hope this helps.
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