Just keep it up about the A. It is the primary, but not sole, reason for this current mess. If she doesn't admit that she's just in denial. A good marriage counselor would probably tell her that in order for things to be worked on she has to at least not be in another relationship. Stay strong for the kids and have some fun with them.
As for the wife, just go about your day and invite her or not as your feelings guide you. Don't go out of your way to communicate with her. You don't even need to repeat about the A, she's heard you as is evidenced by her paranoid behaviour.
I would, however, keep going to the gym. If you have a membership you have a right to use the facilities. I'd probably be just a little vindictive myself and do it during the wimpmeister's time...and look him in the eye every time. No other contact is necessary.
