"I have told you before that I find your affair with OW unacceptable. It is disrespectful to me and our life together. I can't stop you from cheating but I refuse to be lied to anymore. I love you very much, and don't want to break up. I am willing to work on any and all issues, including mine, but I simply cannot do it while you are having an affair. If you choose to continue this affair I want you out of this house."
Thoughts?
I think that's perfect. But don't do it if you're not prepared to accept the risks. Is there a fallback plan you can come up with for a place to stay temporarily?