"My guess is that she has told him we don't sleep together but just share the house and co-parent."
It will drive him nuts because he knows W can't be trusted because she's cheating on her H.
My guess is that OM will see it as some kind of challenge game to him. He wants to win her to feel good about himself. It will be an ego boost for him to win your W. W ego is being boosted because OM knows OM wants her despite her being M. If they ride-off togther into the sunset then he's still going to be wondering whether she had been honest whilst still living with you, and she is going to be wondering if he will cheat on her even with a M woman.
