When a WAW just comes out and tells you she is not going to end the A, it is comparable to a rebellious young adult. They are determined to do what they want to do and the more you try to change their minds.....the more they rebell. Therefore, life has to be the teacher by putting them through hard experiences.
It is not you job to administer punishment or shame, but neither should you try to shield her from it. That means you have to put yourself into a new role for awhile. You are use to being the protector of your family (and will continue to protect you a d the children), but you will need to step aside and let things hit her as though you are no longer in the picture. After all, that is what she thinks she wants, so let her have it. When a M woman wants to play around like she is single, there is a price. I personally believe that the WAW in an A has to be able to see some of that cost before she starts coming to her senses.
The more you struggle to get her to do things your way (trying to save the marriage), the harder she will fight you. That's why some WAW's say they want to be good friends with the LBH, b/c she wants to take the arguing out of the picture and everyone just be one happy family. However, the family unit is broken b/c of her decisions and it can't be a happy family until she ends the A and is willing to work on repairing the MR.
I know it is so easy to get your attention focused on the third party, but many WAW's end an A and still do not want to R the M. But for sure, nothing.......and I mean nothing will be accomplished toward your MR as long as she continues the A. The first step she has to make before you even consider reconciling is end the A and get through the withdrawal period with no contacting OM. She would need to be willing to be fully transparent in all her activity. And transparency really tests the rebellious spirit of the WAW. However, that is a ways off yet.
I said all of the above mainly to emphasize that giving her material to read on M or getting her into MC really is a waste of effort b/c she is not interested in saving the M. Her reasons of "better communication" is flimsy, at best. I can almost guarantee you that no ground will be gained. Now, once she is ready to R, then I suggest a good pro marriage counselor who will work with you both.
Starsky is a succeful DBer, and he could be a lot of help to you. He usually hangs around this forum when visits the board.
Devaste, you are getting spot-on advice here, and I agree with everything Sandi has said. Considering she is a former wayward (EA) wife, and my wife had an active PA (and I saved my marriage and today we couldn't be happier) . . . you're getting agreement from BOTH sides of the fence here.
It's really hard for us, especially as men, to NOT shield our wayward spouse from the consequences of her decisions. Especially when they're so destructive. But YOU CANNOT CONTROL HER (this was the single hardest thing for me to get!!!), and she's going to have to put on her BGPs (Big-Girl Panties) and begin to feel the loss of you.
Until she ends her contact with this other man, you really can't begin to make any demands much less try to reconcile your marriage. Right now you should be in the "protection" phase (financially, legally -- even your physical health); hopefully you will have a chance later for what we call "piecing" (reconciliation), and letting her know what your dealbreakers would be for her to come back to the marriage.
In the meantime, WORK ON YOURSELF. Work on those things that YOU know you honestly need to work on, and any of her PRIOR (pre-A) marital complaints were. I say "prior" because a man or a woman caught up in an affair will often re-write marital history, and distort current truth in order to justify what they are doing. But YOU know, in your heart, which of her earlier marital complaints were legitimate, and which jibe with those things that you yourself know you need to work on.
This will be the hardest thing you ever had to do in your life, but it CAN be done.