I'm sorry, I have to be the dissenter. (I went back and tried to edit so that my words weren't too unkind, I hope that I don't come off as too harsh.) People know what lying is, and he knew that he was going to hurt you. Even if there was no happy choice available, he knew that he was taking an action that he shouldn't and he has to accept the consequences of his actions. He lied, he cheated, he knew he was destroying trust. He has to face the fact that the consequences are not going to be fun for him. And I don't accept that he couldn't love this woman and not have sex with her. Really? Just because you desire someone doesn't mean you have to have sex with them. If that's the definition of polyamory, guess what, I don't qualify.
Yes, it's torturous. But he said that he could just be friends. You took him at his word. If he wasn't brave enough to come to you when he realized that he couldn't handle that, that's on him. Otherwise, we all have to spend the rest of our lives trying to figure out what our partners "really" mean rather than believing they're telling the truth. That's crazy-making.
Ladyintricate, I really feel for you. But you stand at a crossroads, and you have to decide. Your husband is probably polyamorous--if you take him at his word, then he is. Can you live with that? Because you can no longer pretend that keeping him in a monogamous marriage is kind or realistic. From this point on, you *must* accept that he is going to have loving and/or sexual relationships with other women. The question is, will you be wife, or friend? (I'm assuming that, for the sake of your children, the two of you would attempt to be friends if you can't be spouses.)
If you decide to stay in the marriage and give polyamory a try, then you're going to have to try to rebuild the trust. It will be hard, but I know I've seen other people on this board do it. If you go back to therapy, this time try for a polyamory-friendly therapist. They are *so* worth it, and my experience has been that they won't be prejudiced against you if you're not polyamorous, in case that worries you. I think you should also think about the fact that he loves this woman, and perhaps--and I'm trying to be as kind as possible, but think about what I'm saying here--perhaps cutting him off *forever* from someone he loves is not a loving act. You're angry, and you have every right to be. You have had your trust broken, by both of them, and that showed a lack of respect from both of them. You deserve some space to figure things out. But if you decide to try to rebuild trust with him, you should try to rebuild trust with her, too. She made the same mistake your husband made, and is worthy of the same amount of forgiveness. Please don't stay in the relationship if you aren't going to eventually be able to forgive; it's not kind to you, your husband, or your children.
You owe it to yourself to research polyamory thoroughly. You owe it to yourself to do some soul-searching and honest self-examination. Let yourself really feel the explanations that LR gave you for why he might have done what he did; understanding his motivations might help you find your way. You owe it to yourself, your kids, and your husband to be completely aware of what you want, what you need, and where you go from here, and communicate it with yourself and your husband.