Feel really sorry for you OP. This was something I considered before my marriage ended (for other reasons) because me and my ex were not really compatible in bed, though we were limping on, rather than stopping altogether.
It’s bad that he’s telling you about it. It’s been noted on Mumsnet that “mentionitis” is often a sign of someone playing away, which is what is effectively happening here.
But having gone down this line, I think you’d always have to accept it might be a risk. I don’t necessarily agree with those who are saying he can have a full relationship with her and yours has run its course. Being married to someone is different from having an affair with someone, no matter how intense. I can imagine a situation where (like Tom Jones) a man can value his marriage enough to stay in it, even while regularly playing away. And if his wife is okay with it, then it’s none of my business.
I can see why you’re struggling and that you’re jealous, but I think open marriage means that you have to accept he might develop feelings as well. I don’t necessarily think it means he will leave, if there are still things in his marriage that he values. This is what “if you love someone, set them free” means to me. If he loves you, he might well remain, despite falling “in love” with someone else.
It comes down to whether you trust him and whether you can bear this. Obviously you trusted him enough to let him have sex. You’ve asked him if he’s fallen for someone else, and he’s said yes. Ask him whether he thinks this might be the end of your marriage and tell him you want him to be completely honest. If he says he doesn’t want to leave the marriage, ask him why and listen to his response and see whether you find it believable.
I think, assuming he wants to stay, and can explain why in a way that you find properly convincing, then I think you need to set up some ground rules, not about how he feels, but about how it affects you. He’s made it clear he doesn’t want to stop, but it is affecting you, so if you both do want to continue, you need to find a way between you to minimize that. That might include asking him to conduct his affair in a more subtle way and definitely not mentioning her ever in your presence.
I genuinely think there are different kinds of love and that “falling in love/limerance” is a kind of wonderful rush. In our western society, we tend to think of that feeling as being a precursor to a permanent relationship. You fall in love, get married, live happily ever after.
But those things don’t have to go hand it hand. And happily ever after is rare, even more so for second marriages. Some people might conduct a love affair, knowing full well that the person they’re involved with wouldn’t suit them for life. He may be enjoying the rush, but appreciate the life you have together in a different way.
If you don’t trust him and can’t see any way to find a way forward that you can ever be happy with this situation, then I think perhaps you have to leave. But if you can discuss it with him and can find a way to trust that he isn’t going to leave, despite these feelings, and he can demonstrate enough respect for you to modify his actions so that you are not affected negatively, it might be possible to weather this. Him rubbing it in your face is actually more disrespectful than the falling (which is, in a way his own business and if he hadn’t told you and had been more subtle, wouldn’t have been a problem).
The terms of your marriage changed when you decided to have an open marriage. Now they’ve changed again. You can step out any time it’s too painful and should do that if it is. But there might still be a way through. He may not be intending to leave. Up to you whether you choose to try to weather this or not.