I live in Georgia and need to know how to file for divorce and custody of my children who currently live with me but the mother lives out of state in North Carolina.
Does your Wife ever come to Georgia to visit with the children? If so, you need to have her served with divorce papers when she is here in Georgia to avoid problems with Jurisdiction. Once she is served with the papers, then the Court in the county of your residence (and the children's residence) will retain jurisdiction over her throughout the divorce proceedings.
How long ago did the mother move to North Carolina? If it has been less than 6 months, then she has not had sufficient time to establish residency elsewhere, and it will be easier to obtain Jurisdiction over her.
I urge you to speak to an attorney about the best way of moving forward with the divorce action here in Georgia. Remember that time is a very sensitive issue here, as the longer you wait, the more difficult it will become to move forward with the divorce proceedings here in Georgia. Many attorneys offer free consultations.
You should retain an attorney for a divorce when children are involved.
If you cannot afford an attorney, you should look into pro bono services in Athens.
Otherwise, if you've lived in Georgia for 6 months and there is no issue regarding custody, Georgia will have venue for your divorce. You should have access to UGA's law library where you can perform legal research and act on your own.
Also, you may be able to obtain certain forms at the Clarke County website. I've provided a link to that site, which includes a family law informational packet.