What I am about to suggest is harsh and dramatic but you need to consider all your options at this time.
You do not have to allow her to come back into the house, Frank.
That will alleviate the one thing that has concerned me about your sitch and that is that she would stir up some kind of BS and have you legally removed from your home, thereby situating herself all warm and fuzzy in the house with the girls and you out and footing the bill and probably under a restraining order.
Technically, she left and you have reason to believe she is cheating on you. At the very least, she is behaving very disrespectfully since she's right around the corner and all the neighbors are aware of this johnny come lately. At the worst, she might be trying to begin an affair. Her "I can't date because I'm still married" comment was nothing more than her trying to chap your ass into filing because she can't afford to. It wasn't a statement made with a spirit of offense because she actually thinks it would be morally WRONG to date, she made it spitefully I think, no matter which fake tone she used.
I think now is the time for you to seek legal counsel, Frank.