You hung in there and gave it your best shot!! Now sit back and pull back a little. She wants you as a friend and a co-parent on good terms. Start dating and become less available and she how she handles it.
But the more time she spends with you and the girls the less time see spends with the OM. She knows that you will never accept the OM in the girls life or yours. I personally would not be friendly with my wife if she were still with the OM that helped destroy my marriage. And definately wouldn't want him around my kids. If she dropped him and still wanted to be divorced then it would be easier to accept another man later after I had accepted and moved on.
She needs to know that this OM eventually has to go. It doesn't soound like, based on your posts, that she is the type that is madly in love and found her soulmate etc etc. So dropping him shouldn't be a problem. I am more devious and strategic (Retired Military) so I would find all the ways to continue to make it uncomfortable for the OM to continue this relationship!! Though I have to admit he has hung in there more than most would if all he wanted was a booty call. So he could require more extreme measures to discourage him....exposure to his family, co-workers...find out the days/times he can see your wife and accidentally be there of have the girls there etc.
