If your girls were older I'd just ignore her completely.
I'd decline the invitation to be introduced. I know there's all these "rules" about how divorced people are supposed to be friends and "coparent" and blah blah blah but man there aint a chance in hell I'd want to meet the OM for any reason that wouldn't land me in jail. I would ignore him and her outside of your girls.
Glad to hear the new gal is all that Harvey!
H 34 W 29 BD 3/12/18 Divorce Busted Spring 19
It is not things that bother us, but the stories we tell ourselves about things.