I've found "Surviving An Affair" by Drs. Hartley and Chalmers and "Fall In Love, Stay In Love" by Dr. Hartley (MarriageBuilders or MB books) to be invaluable in the path to recovery of my marriage. If you or your wife are not willing to go through the system in these books to recover your marriage then you're still at square 1. Going to counselling might give you a venue to make her see that it's necessary but as Fergie said, if she's dumping all responsibility for the affair on you then you're dead in the water.
Accept 50% of the blame for your prior marriage's faults, but the decision to have an affair was 100% your wife's choice and she has to admit that. She could have suggested counselling, seperated, filed for divorce, and instead she just betrayed you. So I wouldn't put up with laying the affair at your door at all, thats bull cookies. It's all on her!
Once you understand what your respective important emotional needs (ENs) are, you'll understand what ENs you both have to address to stabilize your marriage. In particular I found I needed Affection, Admiration, and Sexual Fulfillment to be healing in my relationship, while my wife needed Domestic Support, Conversation, and Recreational Companionship to meet her needs.
We ended up going to the MC about 6 times plus a few IC sessions and the net result was by applying the MB books we were way ahead of the game and started recovery and healing much faster than with MC alone. My MC used the Gottman method which has some good points to allow structured discussion of the affairs (Atonement) and is focused on communicating, but we didn't get too far into it. My MC asked for links to the MC books LOL. I won't rule out going to the MC again if we find we're in difficulties but I wouldn't let the MC drive the pace of recovery, I found it agonizingly slow and just kept us in painful limbo longer.
Use the MC to work through problem areas like communicating but with the MB books it was pretty optional for me. YMMV.