Note : Your wife my call you on the hardball and just say "OK, I want a divorce now then..."
Just say "I am sorry you feel that way, you can pack your things now, I will have the rest sent over"...
If she says she has nowhere to go :
"You should have thought of that before you started cheating on me... I offered to work with you, but you seem to think cheating is more constructive... So, bye bye"
"I won't be filing for the divorce, I didn't want one... And I didn't agree to an open marriage in this home when we moved in... And I don't agree to one now... Pack your things or I will pack them for you"
SOmething like that... You want to catch her off guard... SHe's probably expecting you to beg her to work on the marriage...
Call her bluff and start packing her things... Don't stay in the convo... Just find some boxes and start packing...
