I recently began a relationship with a man who is going through a divorce. His wife lives in Texas and he and I live in Georgia. Even though they decided to divorce before I met him, and have been separated for several months, she is angry because she found out about our relationship and is threatening to legally prosecute me and has even hired a private investigator. I am aware that adultery is considered a misdemeanor in Georgia, but does this mean she can prosecute me, him, or both of us?

Sicko is it

I doubt it.

Even in GA, they do not even use that as a crime anymore.
While still on the books, it is not used to my knowledge.
GA has many laws that are obsolete and some that are not even inforceable.

So no, she will use all that info against him in divorce court.
Personal advice, stop seeing this man till he is actually divorced