P.S. And if it IS (a dealbreaker, that is), you don't ASK her, you TELL her: "Look, I've been thinking about this, and I have a real problem with you continuing to talk to other guys while we are separated. I want to WORK ON OUR MARRIAGE -- including my own contributions to the problem -- but I can't do that while there's a third person in it. I get what you're saying about wanting to continue to see changes in me, and waiting for your feelings for me to return, but these are really two separate issues. One is a DECISION -- a commitment -- and the other is feelings. I'm willing to be patient for your feelings to return, and to believe the changes you've seen in me, but make no mistake -- I am NOT willing to live in an open marriage in the meantime."
You don't ASK a spouse "oh please be faithful to me." You TELL them, "I cannot live in an open marriage." Then it's up to them to decide what to do with that info -- you can't control them.