everyone's sitch is different. The characters are different. There is not a one size fits all for this. In YOUR particular sitch, she YOU need to enforce boundaries and make it clear that you WANT her to leave. You may not be able to make her, but you should let her know that you want her to.
My cousin is having an A. Her H doesn't know about it, but he knows their M has been failing for a long time. he says ridiculous soft things to say save it, and she has said "his pussiness is so unattractive to me" I bet maybe if he would man up a bit, he might just have a fighting chance.
Truth be told, my cousin has always worn the pants. Always been in control. She is the bread winner and decision maker. She is seeing an older (married) guy, but she views him as a man. She is head over heels for this guy (none of this is going to end well and she knows it) but I have never ever seen her relinquish control and emotion like this before.
So, stand up for your M, be a man, not a guy who tolerates his wife running around him. Because she is. And the two of you separated under the same roof mean she has an excuse in her head that openly being with OM is fine now that you are separated, and you are present to take care of everything.
Heck, this might be the best situation imaginable for her.