Think about this objectively. OW knows his situation: that he's been married a long while, is STILL married, has young kids and is moving forward at break neck speed with adultery. What kind of woman would involve herself in this situation? A broken one. Your h is broken right now, he has no way to attract a decent woman because no decent woman would touch this situation with a ten foot pole.
She is the one who is humiliating herself, as is he. And if it's a small town, everyone will understand exactly what this all is. She is far, far beneath you.
My advice? If you run into them, square your shoulders, hold your head up high and don't show them a care in the world.
As for your kids, if he asks permission, my advice? Politely/calmly tell him no, you'd rather be didn't introduce them out of respect for the fact that you are still married and you feel it is disrespectful to pattern adultery to children. Of course you can't control his decisions but I know in the past he's wanted some of your approval and he's asked for it under some bizarre scenarios. Weird, but they are all odd in different ways. Maybe, he will honor your request. If not, maybe try to get your kids to a good therapist?
I am sorry. Their empathy chips are busted and they operate on emotions only.
Crazy as this sounds, it has nothing to do with you even though it impacts you so much. Maintain your dignity and be thankful you are not as broken as them.
Me 41, H 47, M 15 yrs, S11, S13 BD 1: 11/4/14 we work on it; really I pretzel myself BD 2: 3/31/15 H goes down to "dorm room" 8/15: H back to MBR 10/15: H back in dorm room 1/18: H files, now divorced