I haven't read what everyone else said, but I can relate to your wife in a way. I have a boyfriend who is my other primary (Mono). There have been times when I lead a separate life from my family (PN and my boy). I have fought hard for that to not happen. It's so easy to slide into that as time goes on. When everyone becomes complacent in the relationship and hums along without working on these things, it can be so easy.
When I am at home with PN I do all the things that we used to do as a family. Little to nothing has changed. He has not noticed that I have changed because on the outside I look and act the same... but I have. I have another life. I go to my other home (the OH I call it) and I lead a different life. I do similar things I did when I wasn't married or raising a child and was living with a boyfriend. Mono and I have a whole other life...
I have asked for a long time that the two worlds merge. Even though I love both my lives. I don't see any way of moving into the future without a merge happening. We are right on the verge of that.
I think it has been necessary to see if we are all compatible and that my relationship with both men is worth working on and sustaining,,, thriving in. We worked on it in two ways; my spending time in my other life with Mono and coming together as a whole unit and spending a lot of time together as a group.. a family. It's been 18 months of working on it and we will all be in one house (Mono and I in the apartment below).
I really think that if your wifes situation is to work for an extended period of time with the family you have created together then she will have to start merging her lives. It might be working for her to go to another home and live her life their but it isn't working for you and that means that it won't work for the future. If there is someone struggling in a relationship dynamic then the whole thing will eventually cave in on itself if that isn't worked out.
Of course if you decide that you would rather this man not be involved with your family then you would have to come up with how it would work for you and she would have to work out how it would work for her.
My experience has been that I find my heart strings pulled across the city. If I am at home I miss Mono terribly and feel like something is missing... like I am away on a business trip and miss home. When I am with him I feel the same. I miss my child, feel guilty for not being there, guilty for not pulling my weight at home and leaving it to PN, and absolutely desperately in agony when once my boy had to go to the emerge and I wasn't home to be there to take him, and be close to my child *tear*
I didn't like that at all!!!
The difference I think in your situation is that PN is quite happy my living two lives as long as we all come together and spend time together. Perhaps this is what will work for you? He wasn't and isn't all that keen on Mono moving in I don't think. I think he sees the advantages now but is scared of the changes to come. I am too, we all are... but we will try it, and adjust as time goes on, into something that works.
If you want to read a bit more about it I have a blog in another section.