Ovrrnbw, I can sympathize with how hard it is to take bold action and kick out your own wife especially when she's crying and acting pitiful. You love her and she's your wife so it's not easy to do such a thing. You have to be mentally prepared and believe in what you're doing. If you didn't do it last night it's not the end-of-the-world given this has been going on for so long. Your wife obviously has issues and nothing will get solved in one night. It's worth really thinking though about what's within your power to do to end this situation. When my husband decided to move out last year he saw me suffering but he ignored my reactions because he'd already made up his mind. I guess you have to make up your mind. You could keep letting things progress naturally and see what happens. Your wife might break things off with OM on her own, but in few years she might meet some other amazing guy and she'll remember how easy you were on her when she cheated. She'll probably think she can get away with it again. Or if you let your wife do as she pleases and hope for the best you'll both be ignoring the core issues as to why this happened in the first place.
Last winter it was easy for others to say I should divorce my husband not wait for him to file or do it first, but I couldn't do it. I wasn't convinced it was the right thing to do because I didn't want to be held responsible for the demise of a marriage that I wanted more than anything to save. We all have limitations and we also get tired to a point where we don't have the energy to battle with our spouses or care enough about what will happen in the long-term if we can have them back in the short-term.
There's always a chance your wife will work everything out on her own and she'll be back, loyal and committed, in the near future. Waiting for that to happen is definitely easier if you feel you can handle her sleepovers at OM's house in the meantime. It won't really fix the core problem though.
You know your own situation best. It's easier to see from the outside that taking a strong approach and sending your wife to live elsewhere is the best way to fix this, but it's still your choice. You sound like a good man and you deserve support no matter what you choose.