Walloped,
I come around infrequently these days, wanted to toss out a couple of random tidbits.
No fast track on this. It is a slog. A marathon. Fast tracking = rug sweeping. Even if it all gets laid out there, there is still the processing. There's intellectually knowing you can't go back to the world before the A, and then there's living it.
You will be consumed with "why". I still am at times, 30 years later. I've learned there is no good enough answer to the "why" question, in that what you come up with will never satisfy you.
But that also it is not that hard of a question to answer, it's just you never like the answer. The answer to "why" is because she wanted to, and she thought she could.
So why did she want to? The answer to that lies within your own experience. Revisit the impact on yourself (literally, your Self) that you felt when you found out. The A is an attack on Who You Are, which was and is tied to your WW. A crushing blow on your Self. Well, the opposite of that crushing blow is the gigantic ego kibbles your WW got from the AP. Her Self gained tremendously from the A. The depths of your low gives you insight on the heights of her high.
Was he better/worse/uglier/more handsome/funnier than you so she could do this? Here's the deal. If you had an unknown twin brother who was like you in every possible way (except for he wanted an A for some reason) and he came on to your wife, so he offered absolutely nothing different from you other than a new blast of attention and affection, would she have taken the bait. Yes. It wasn't you.
How could she compartmentalize it? We're adults...we compartmentalize our lives all the time. How we act in one setting differs from another. We have deep, secret lives of our own. For a time, you and the kids were a supporting actor in her story. She was a master of the universe, cake eating to her heart's content.
I'm not a big fan of counseling to figure out "what is broken". She had feelings, which are poorly controlled. Will IC attempt to manipulate the feelings? Can you manipulate yours? Can you turn off your anger right now? And your love for her? If not, why do you expect her to? Does your R depend on that? It's a low probability of success.
Better in counseling to focus on what she controls 100%. Her actions. Not her feelings. Her actions. Changing feelings is like an exorcism. Changing actions is just being an adult, owning your shit, and doing The Right Thing. The beauty of putting actions first, is actions influence feelings.
This goes for you to. Your feeling are everywhere. Attempts to control them directly fail. But you CAN control your actions. You know what needs doing, just do it. The 180 is about this. take control. Do what needs doing.
The sad thing about all of this, is the marriage is not hers to heal. It is yours to heal. If your wife does absolutely everything perfectly in the steps leading to R, you will find that you are left carrying the tremendous burden of closing the final wounds and moving forward. It's not fair, it's not right, it is just the way it is. Is she worth it? Can the burden of this past be overcome? You can well know right now the answer is 'no'. Figuring out if the answer is 'yes' takes real time.
My WW's affair was almost 30 years ago. I love her, she's never, ever come close to doing this again, the scars we both bear are deep. The A informs everything in our life, good and bad. We are the crooked timber of humanity, after all.
Be patient, my friend.