He sounds like he wants to eat his cake and have it, too. Too many men have even admitted that they would live like this if they could. Some feel they won't get caught so this is what they do - for as long as they can get away with it. And, of course, they'll deny their "cheatin' ways" - even to the point of trying to make you think you're imagining things. That's scary when a person plays mind games to the point that they try to convince us we're "crazy" - when they know very well we're not. Then if we have proof/we catch them in the act, they move on to some other poor unsuspecting woman who doesn't truly know them yet.
One of the reasons we "forgive and forget", take them back, go back to them after we've left them is because they weren't always bad, they weren't always cruel and hurting us. We remember the good times, forget the bad, and take them back when they apologize (and their apology is easier to say than finding a new "victim").
I wonder if your partner's ex-wife's boyfriend (confusing, isn't it!) knows she was cheating on him! It sounds like your partner and his ex deserve each other. Personally, I say: cut 'em all loose. They're not worth the grief, hon. The fact that he goes back to her looks like he's just using both of you (and who knows who else he's having sex with).
It takes a lot of strength to stay silent sometimes. Unfortunately she doesn't have your strength - hence calling you names. She feels threatened by you (and probably anyone her ex-husband is with) and is jealous that he divorced her but still uses her for a free orgasm/to "scratch an itch", and he wants you/he keeps going back to you. That just ticks her off and she takes her frustration out on you.
Whenever she tries to make you feel bad, please remind yourself that you haven't done anything wrong. You haven't cheated on your partner, you haven't stuck it under another woman's nose to try to make her feel bad. You have the right to look down your nose at her. I know she may still love him, but real women don't treat other women the way she's treating you.
You also have the right to feel sad that you haven't reached the point, yet, where you feel comfortable leaving him and staying away from him. It may happen one day. And if it does, it won't bother you to see him with someone else (the way it bothers his ex when she sees him with you).