I agree it pays to take a firm line at the outset. You may want to think about something like:
I'm not willing for you to remain here if you are disrespecting our M and our family by conducting a R with someone else. It's your choice what you do, but if you want to remain involved with OM, you'll have to leave this house today. I will be staying here with the kids. And you have 10 minutes to decide.
I'm not a vet and haven't been in this situation - so don't treat this as 'expert' advice....have you seen any suitable scripts on the site? Starsky's normally good for this kind of thing of course.
Just a tip, when my H was having an A and I was suspicious. He'd get cross with me for being suspicious and paranoid. Said I had to stop with all that and I should move on (from the discovered EA that he said ended, but had turned into a PA.) He made me really doubt myself at the time - no more of that now for me of course!
Family leadership - your W may not like it at all, but I think it's what your sitch needs! And keep very calm and very strong.
T 13 M 7 Me 48 H 46 SS 15 BD 7.14 PA D final 5.16 (H filed)
We receive & we lose, and must try to achieve gratitude & embrace with whole hearts whatever of life that remains after the losses - Dubus