, I am so sorry that your wife has hurt you like this. There are many here who understand your feelings all too well.
As to whether you can find a way back to a place where you could consider staying married, I'm afraid that only you can answer that question. Many have and many haven't. People who heal from the awful pain caused by their spouse's infidelity can do that from inside their marriage, or by simply letting their marriage go. Some of us have made the journey with our unfaithful partner's support. Some of us haven't had that, or haven't even wanted it. But you don't have to decide any of this now, and you should take as long as you need to decide. Your emotional state
I went from being neutrally OK(ish), to feeling love for my husband and wanting my mariageto survive, to wanting to divorce my husband, several times a day when I was working things through in my head. Feeling like you are being irrational and oscillating between feelings of desperate love and then great sadness (and probably enormous anger and bitterness - if not now, then with time) is completely normal. You are trying to internally reconcile the person that you thought your wife was, with what she has done. You are trying to find a way forward. You are trying to understand all of the consequences of whatever decisions are available to you. You keep "forgetting" and normal life takes over for a little while and then you remember again. And then it starts all over again. Don't expect it to make sense, no part of this "makes sense". If you can afford it, I would recommend that you go for individual counselling (IC) as well. Remember that your MC's patient (if they are good) is your marriage, not you. You need someone who is completely on YOUR side, and is focused on helping you understand what you need and want. If you can't see a therapist by yourself, then do you have a good and wise friend or religious confidant that you can talk this through with? PA or EA?
I'm going to get shouted down by many on TAM saying this, but I do believe that it is possible that your wife did not have a sexual PA (I'm not going to comment on hugging, kissing etc.). (Although, I don't personally see an EA as a far lesser betrayal.) My husband's morality was not the same as mine. In his mind, as long as he didn't have sex then what he was doing "wasn't so bad". It was wrong, but not an incredibly damaging betrayal (in his mind, NOT mine). When I found out about my husband's second betrayal, I asked him to have a polygraph but backed down once we started working through things. When I found evidence of things that he had "under-represented", he offered to take the polygraph himself. And he did. And it was humiliating for him and very painful. And I'm glad that it was both those things. Because by doing it, he proved some things to me. Firstly that he was (in all likelihood - polygraphs are not 100% guaranteed) telling the truth; and secondly that he was willing to do this to prove how committed he was to helping me recover my faith in our marriage and his commitment to it. He was ashamed. This was a good thing. (If you want some more info about my polygraph situation, please just ask.) Disclosing to the OM's wife
Absolutely. (If you had done this when you first found out about what had happened, then it is very likely that the relationship would not have continued. Your wife may very well have just found another place to get her emotional high, but she may not have. (A lot of if's and but's here.) Don't use disclosure as a threat against your wife. The OM's wife deserves to know. Just like you do. You are disclosing because this is the best way to make sure that the affair stops in its tracks. Shine a light on their behaviour - let the full weight of consequences come to play. Their choices were neither morally acceptable nor constructive, and meeting their behaviour head-on is the best way for them to face up to what they did. Just forward what you know to the OM's wife. In my case, the OW's H told me enough to get things out in the open. Do I think he did it in anger - absolutely? But I am also very grateful that he did do it. Consequences and honesty
Your wife is still hiding behind thinking that there could be a good reason why she did this to you and your family. The lame excuses - that is her trying to come up with a reason that makes what she did acceptable to both her and you. She is trying to avoid telling you the truth because it shames her to confront it. She enjoyed having him declare his love, tell her how much she meant to him; and she welcomed this, even knowing that it was wrong. Knowing that it would and had hurt you. She did it because it made her feel good. Because she thought that she would get away with it. She didn't just cheat on her wedding vows, but she stole from you (because all that emotional energy and connection belonged to you). She has a very long journey to make on her own to understand herself and her actions and choices.
When I first asked my husband to take the polygraph, he got frustrated and angry. I remember him sitting on the edge of our bed saying "Why do you want this? I've told you the truth. Don't you trust me?" I answered, "No. I don't. I may never trust you again." I think that was the moment that he finally began to understand what he had done. Your wife does not currently deserve your trust. To tell you that either you trust her or you should separate? After what you have found out? It's not just unfair, it's ridiculous.
Your wife wants you to let this go (like you did last time). I did this the first time with my husband, as well. You were neither gullible nor naive because you did just that. Your wife said that she loved you and was very sorry for what she'd done, that she would never do something like this to you again. You loved her and you trusted her. You took her promise at face value. Unfortunately, you can no longer do that. If she threatens separation to prevent the truth from coming out, then she is more concerned with her reputation (and the OM's) than she is with the future of your marriage. She is still living in the place where if you close your eyes tightly then the bad stuff goes away. You don't live there.
My thoughts are with you - your situation speaks very closely to me. Be strong.