I wish you hadn't had the R talk with her, and advised against it. You've given her ALL of the power back. What jumps out at me from your conversation is how many times you keep asking HER what SHE wants. Until you're ready to express, in a strong but loving way, what GOODGUY wants, she will never respect you.
And women tie "respect" VERY closely with "love" -- in fact, most women cannot love a man deeply if they're not feeling respect for him.
If you ask her if she's been faithful to you, and she has, she will say "yes."
If you ask her if she's been faithful to you, and she hasn't (and I don't think she has), she will lie to you, and say "yes."
See your dilemna?
Cheaters always lie -- period.
Here's the other problem you have: if she IS cheating on you, then nearly everything she says to you is a lie at worst, or is "spin"/"re-writing of marital history" at best. And yet you are now going to try to use it as data from which to form a foundation for your strategy and tactics moving forward. That won't work.
Did she ever have a serious conversation with you BEFORE last fall, when she suggested a separation? My guess is that she was already involved at that point.
I don't mean to be all negative -- there's a lot you did right. You refused to reveal the source(s) of your intel, but yet remained absolutely firm that you knew all about her and OM. EXCELLENT.
You told her you weren't going to move out of your own house. EXCELLENT.
Where you lost control was as soon as it started to veer toward an R talk, you should have cut it off, and said "I don't want to talk about this now. End your affair, and we'll talk about any and all issues, including mine. Until then, there's really no sense discussing it."