I don't know if I agree with you that Poly cannot work where one relationship is "fucked up". But I can feel the pain in your latest posts. I read your post a few days ago when you were feeling really good and I was tempted to post a cautionary one but I thought who was I to bring you down.
The reason I say that about a poly relationship not being impossible when the relationship is troubled is because I was in a very similar situation to your wife. My marriage did end because my husband couldn't handle me loving someone else but looking back I wonder if it could have worked. Not long term. Her relationship with him won't last, I can practically guarantee that, but as an interim thing to help you through.
I know this sounds very strange and you can call it bs and ignore it if you like but I'm going to share it with you anyway. I had got to the point where I could no longer feel love for or from my husband. Too much crap had gone down between us. Our relationship was like a clogged up, polluted creek. The love I received from my bf, or kindness, attraction - whatever it was - fed me emotionally so that I had something to give back to my husband again. It got our emotions running again somehow and began to show me what a healthy relationship looked like.
You would have to work at it really carefully and she would have to be willing to try but it could save your marriage. Marriages, especially where children are involved are worth the work I think. I'll tell you more if you're interested.
i also wouldn't be at all surprised if your wife agrees to give up her bf. Your financial responsibilities would make it very difficult for her to go solo and you probably know that. When push came to shove I did jump the marriage ship but my youngest was 17. It was still very hard.
My thoughts are with your whatever you decide to do.