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If there is no formal separation agreement in place and no order from the court then there is nothing stopping you from visiting your children. The default in GA is that both parents have joint custody until a judge says otherwise through entering an order.
However, the fact that you did not sign the divorce petition will not stop her from proceeding with the divorce. If you do not respond and formally oppose her petition, she will eventually get a default divorce and will get everything she has asked for in her petition.
So you have to respond and oppose it or she will get what she asked for by default.
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