You told her she could "have him" under your terms, ie: leaving the house...
If she isn't quite sure she wants to commit to that, she can turn it right around, act all sweet and nice, be the "wife" you want her to be, all the while still talking it up with him via secret cell phone or secret email account or fake FB name etc...
If she wants to cheat, she is going to cheat and there isn't a darn thing you are going to do about it.
May All Who Seek To Take My Life Be Put To Shame And Confusion; May All Who Desire My Ruin Be Turned Back In Disgrace. ~Psalm 40:14~