Keep in mind that this is only my opinion, but if you are not going to reconcile with this man, the best thing to do would be to move. Change your phone number and mailing address, start over new somewhere else.
No he can not get out of the agreement unless he has something from a doctor saying that he was under too much mental stress to sign an agreement…then he may have a shot at getting out of it, but regardless the last three months, he would still be held accountable.
If he has continually gotten out of paying you due to excuses about paying her then yes, proving that he’s living there may help. It would show, first, that he’s an adulterer, and second, that he’s lying to you to get out of supporting you as he agreed. Keep a journal of dates and events, record phone conversations…document, document, document.
My original suggestion is the only one I can think of about getting her “out” of your life. Sometimes, the best solution is not to fight the battles at all…