JWM Sorry to see you in this situation. I was where you are now couple months ago except I never reached an agreement with my W before she left. Your W is only one can decide 'No contact' to the OM.
This is true. However, only JWM can decide whether or not he's willing to remain in a marriage where his wife is still contacting another man, after she promised not to, and convey that to her in a loving but matter-of-fact way.
That's the difference between "controlling" and "boundaries." Controlling is telling another person what they can (or cannot) do. Boundaries are telling another person what YOU are (and are not) willing to abide, as a matter of personal integrity.