OK, first of all you need a new name, LOL. I think you should confront your wife; why wouldn't you? Isn't this very serious? No shouting, no angry outbursts, just calmly tell her that "I know all about you and ______ , and it needs to stop. It's incredibly disrespectful to me and our marriage (and if you have kids, throw in " . . . and our family.")
Do NOT tell her HOW you know, only that you know (never reveal the source of good intel!).
All you can really do at this point is let her know that you're NOT willing to live in an open marriage (a boundary); what she then decides to DO is completely up to her (you can't control her).