I really feel because she wants to end our marriage she must be the one to leave. My question is òwhat do I do if she acknowledged the affair, but refuses to leave when I tell her I no longer want to live with a cheater
I admit I don't have any personal experience in this aspect. You can't physically remove her from the house...however you can remove the stuff. She leaves for a few hours or a weekend, you pack it up and move it out. It must be quite the shock value to come home to all your stuff on the back porch or in the garage. She would likely throw a fit and call you every name under the sun, that is when you stick to your boundary of not living with a cheater.
From what ive read on here, she must be the one to decide to end it, it won't end if its a demand from you. She should come up with the plan to earn your trust, etc...she does the work. She probably won't just want to work on it as soon as she knows that you know...shouldn't have to worry about it tonight. But work on a list of "must haves" before you'll consider any sort of reconciliation and stick to your guns.
Me40; W38; S12; D9 BD11/19/2018 D filed 12/20/18 D Final 7/2020 Being the best example I know how for my kids to see.