"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.")
That's kind of what this is. When the spouse has almost completely checked out, I'm just not sure about "needs to stop". It all depends on where she's at with this. I would do that if she was still at least faking she was still in the marriage, but where it sounds like she's checked out and will just say, "I've told you I want divorced. I don't consider myself married anyway, so you really have no say about it."
Was your wife sneaking around without talking about divorce or was she talking divorce already? That's why I said, "wasn't sure" if I'd do that. Maybe you are right that it still needs to be said. I would probably be more like, "I know all about it. I can't control what you do, but it's disrespectful and I don't want the kids around him and I don't want to even be friends with you under these circumstances." Just kicking things around here.
You cannot be lonely if you like the person you're alone with. Dr. Wayne Dyer
When the spouse has almost completely checked out, I'm just not sure about "needs to stop". It all depends on where she's at with this. I would do that if she was still at least faking she was still in the marriage, but where it sounds like she's checked out and will just say, "I've told you I want divorced. I don't consider myself married anyway, so you really have no say about it." 