she isn't trying to say anything to you, she is looking for a more comfortable place to sleep, stop thinking that everything has to do with you, it doesn't.
I would bust her on that behavior though, is your son going to sleep with you now for the next couple of years until this is resolved?
NO.
Tell her, that is your son's bedroom, that is where he sleeps, your daughter sleeps in her room, you sleep in the master bedroom, she sleeps on the couch, you have decided that that's how it will work in your house from now on, if she wants an affair with another man, she can go sleep on the couch or actually find another place to live, that would be better, just tell her "no offense but I don't need you messing up the rest of our family's lives because of this affair of yours, also I've decided we're telling the kids tonight about this so that no one is in the dark about the situation anymore."
Also, the allure and the excitement of the extramarital affair is fueled by it's..... secrecy. That's what makes it so exciting. Reveal the secret. Contact the OM, tell him you know, tell him he can have her (seriously). Does the OM have a wife? If so, contact her, let her know what's going on.
As for your kids, tell them that you and your wife are getting a divorce (don't tell them about the affair, you can let your wife break their hearts with that nugget, that part isn't your job).