Does anyone have any advice on this? Can this still be worked out from separate households or is it time for me just to move on?

It has been a while since I last posted but things are still much the same. I need some advice on what to do next.
She has moved out but has continued to stay in contact with me the whole time. There are phone calls to check on me and daily e-mails going back and forth. The problem is she has admitted that she is still seeing OM and that she never actually broke it off. About a week ago she asked me to go to dinner with her and I told her only if she sent the NC letter. Needless to say she did not send it and we did not have dinner. She constantly tells me that she is unsure of what she wants but she wont cut him loose. She has even introduced him to our daughter, which did not go well. I have tried to do things for her following a plan A but it seems to have little effect. Should I move to plan B or just cut her loose?
I got so depressed that I was thinking very unhealthy thoughts and I am now seeing a therapist that is trying to help me pick up the pieces but the constant signs of hope from her are killing me. It seems like my progress is set back each time I talk to her. I have asked her if he knows that we are still talking about working things and she replied that it was none of his bussiness.

Where do I go next?