I’m pretty sure that under the law you can divorce a man you don’t want to be married to. You don’t have to earn that. Not anymore.
But that aside.

Matt, your wife is acting like a jerk. “It’s just talk”? No, that makes no sense. She wants out of her marriage. That’s what she’s telling this guy, that’s what she’s telling herself, she just can’t bear to tell you. Yet.

Sorry to give you bad news, but from what you’ve said, I just can’t imagine this marriage working out. At all. Never mind if poly marriages are taboo – it’s not what you want. And poly relationships work only if all members can count on each other to be truthful and each of the members are devoted to making it work. This is not going to work. If she doesn’t have a change of heart dead quick and starts working on gaining your trust back, I don’t think there’s any way out of this but filing for divorce.

There’s worse things than growing up in a single-parent marriage. And maybe you can find someone new in time to be a mother to your kids.

This is tough, man. I hope you have people you can talk to while you go through this. Know that things won’t always hurt this bad. Keep moving. All my best wishes.