You are having an emotional affair.
I have personal experience with this.
If you want to save your marriage, this is what you do:
1. Cut off all contact with the AA woman. This includes meetings. Do not go to meetings she attends with the idea that you "need a meeting" and she is just another meeting attendee. Go to different meetings. If she shows up at a meeting where you are, LEAVE.
2. Start spending quality time with your wife. Go out with her. Take her to dinner, movies, whatever it is that you two enjoy doing together. If a vacation is possible, this would be an excellent time to go....without the kids.
3. If the above do not help, seek professional counseling ASAP.
Above all, do not listen to the voices in your head telling you that the AA woman is your "soulmate" and there is something wrong with your marriage because you met your wife in a bar. These things are justifications....and since you are fundamentally a good man, you know it. Hence the confusion.
Bottom line: break this off NOW.