Your instincts are right. This situation is not tenable and does not have much merit for anyone in the long run. The real question isn’t what your wife is going to do, or what her lover wants or doesn’t want, but what are your needs and limits?
I would highly recommend individual therapy for you at this point. This will help you sort through your feelings independent of everyone else’s. You listed what you wanted to have happen above — but it all had to do with what you want your wife and her lover to do. The real work here is for you to stop hoping things will change ––and start thinking about what makes sense for you given the current situation.
Tolerating your wife’s ongoing unacceptable behavior and extending yourself has reached a limit. She has only been able to be marginally available to you, and continues to text, email and for all practical purposes stay emotionally connected to her lover. She has not respected your needs. You’re wife has made a series of very poor decisions with regard to you and your family. It is time to start thinking what you need to do, not what you hope your wife and her lover can do to help you feel better.
In individual therapy I would explore what your limits are. I would ask yourself if your feelings for your wife are still the same after the disappointment she has caused and continues to cause. Has your love for her changed at some fundamental level? I wouldn’t put the emphasis on what she should do to help you feel better. I would rather see you sort through your own feelings and find ways to manage them.