She has no interest in seeing a MC in order to save the relationship. She will simply use it as a "safe place" to announce her decision to D.....or she will use it as her excuse, "I've tried everything...even MC and it didn't help". MC will not help a couple unless both of them want to put 100 percent effort into the MR. Your W doesn't want to save the M.
FWIW, people who are in an EA/PA usually lie a level less than what really happened. For an example, she said it had only been two months, but you traced the calls back to January.
Sad to say, but you really can't believe anything she tells you right now.
Does your W work outside of the home? If not, then I would suggest that you not contribute to a lot of housework, unless she is ill or some other legitimate reason for her not doing it. After all, if she's a homemaker and you are the breadwinner, you won't win any brownie points for doing your job and hers too. However, you can put plenty of time in with the kids. The job description of parents covers both of you. But I don't think I've ever seen a M saved due to the H doing more housework.
About her twin sister......don't trust her for a minute. I would dare bet that she is a very bad influence on your W. You may not be able to control your W visits with her sister, but you better not trust either one of them.
I'm not telling you this in order to add to your pain. I'm telling you in hopes that you won't be set up for more pain by putting your trust in your W or the people she has started associating with lately. As of now, you know that her sister and the OM or two of them. Your W is going to play on your controlling ways big time. That will be her weapon to use on you. And, if you aren't careful, it will work on your mind and you will start thinking that you have to "prove" that she can trust you. That kind of mindset is really messed up, but I've seen it happen over & over again with a LBH who has a W in an A. Remember, she's the one who should be proving she can be trusted, not the other way around.
You need to do some Internet reading on a subject called PEAS. It explains how EA's are like an addiction. I had never heard about it until I came here. The information is true and very real. It may help you for things that may come.
She will try to take the EA to a more hidden level. Especially if the OM has told his W that he won't leave his M.
I'm not going to say much more right now. I know you have to digest this, but things will start moving very fast. You need to be prepared for anything & everything you thought would be your worst nightmare. The LBS has to be prepared at all times. Otherwise, you will make matters even worse.
You need to find the chapter in DR about the LRT and read it immediately. This is what you need to be doing.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!