Warpedatticus, I'm so sorry this is happening to you. As a fellow BS, one with little kids, PLEASE tell his wife. She is probably in the same position as you are, feeling something is amiss, but being gaslit by her wayward spouse.
I had an inkling something was up, but I was sleep deprived and utterly exhausted. I thought I was "taking one for the team," while my fWS was working longer hours. We needed the money, so more overtime, while not ideal, was good.
It was a slap in the face to find out the extra "OT" pay he was earning was him actually spending money on some co-worker. Hotels, dinner, drinks. Meanwhile I was at home, trying to stretch our tight budget, and rewarding myself once a week with coffee or a pastry at the coffee shop near the bus stop where our DS got off from school.
Please. Tell. His. Wife.
You are not the only betrayed person in this situation. She deserves to know. Because I can guarantee you, while he's hanging out late with your wife, she's probably at home doing chores/putting the kids to bed/thinking her husband is "working late," because they could use the OT, too.
I know this is hard. I know doing anything that could push your wife away feels counterintuitive. But the best thing I did was kick my fWS out, file for separation, and start taking care of myself.
You deserve to be with someone that WANTS to be with you. No doubts. No resentment. No guilt trips.
It's really hard when you feel so sad, when your self-esteem has taken a hit, and when you still love the other person. But do you really want to be with someone that doesn't know if they want to be with you?
Take care of yourself. Show your wife what the reality of life without you is like. Right now it's hikes and runs, thrilling secret texts, romance and mystery, and probably sex with her boss.
But she's not dealing with the reality of the situation -- does she want to be an instant stepmom to three little kids that are going to resent her for what she did to their mom? Is she prepared to be judged by co-workers, friends, and families for being a liar and a cheat? Will it still be all fun and romance when half of her affair partner's wealth is being spent on child/spousal support and lawyer fees?
Kicking my fWS out was the absolute best thing I did. He moved in with the other woman, and very quickly realized she wasn't his soulmate -- she was jealous, aggressive, controlling. She gave him a hard time about spending time with his kids. She was no longer an understanding shoulder to cry on, and would get angry if he mentioned me.
You're young. You don't have kids. You could walk away, get some therapy on your own (maybe figure out why you're attracted to women that have wayward traits, and how you can notice red flags?), start over.
But if you're not ready for that, read up on the 180, Dr. Harley's plan b, and going no contact. It can feel weird or counterproductive, but if you want to save your marriage, those three things will help you so, so much.
Stop protecting someone that doesn't care about you (and right now your wayward wife does not). Protect yourself. And please, figure out a way to tell his wife.