I'm on my fourth chance. Maybe things change, maybe they don't. It sounds like he's realizing he's REALLY losing you. So sad for him that he didn't make the right choice with all of the chances you gave him.
I think you know what is best for you. Your deciding weather your willing to dance with him again... maybe doubting your own instincts and letting him let you believe it's best for the kids. Should the kids have hope mommy and daddy are getting back together??
If you really do not want to do this.. maybe think up some reasons why hanging out together will NOT help the kids. Like, a pros and cons list.
Good luck. I know this is tough stuff.