I also hate to be a downer but there is so much wrong here that I question whether it CAN be fixed.
The "long history of lying" coupled with the previous affair AND his current desire for relationships with other women within AA really do not bode well. At all. No wonder you don't trust him any farther than you can throw him.
At least you're in marriage counseling -- I guess his willingness to do at least that much says something positive, and if your marriage can be salvaged, that's the place to start, I would think.
Good luck and take care of yourself. We're here to provide support when you need it.