It doesn't sound to me like the hubby is going to agree to closing the marriage. He's too attached and the pull of NRE is strong. If he does agree, he'll probably resent you for it for a long time.
Also, I think it's ethically wrong to "agree" to a partner dating, then pull the plug completely because it makes you uncomfortable. (I realize there's some ambiguity here because you initially only agreed to one makeout session, but it sounds like this progressed well beyond that before you made much of a fuss.) Perhaps his "work wife" is asking too much of him, but you don't know that -- your hubby could be telling her you're fine with everything. It's not her fault if he's doing crappy things like leaving you with chores so he can go console her with chocolate after a bad day - that sounds like something he initiated, and it's not her job to say "but what about your poor wife and small children"?
It seems like you have two views of poly that need to be reconciled here. One view is "everyone is free to do what they want to do, so he doesn't need my permission." It sounds like there was no explicit agreement up front to be mono for the past two years; it just kind of happened. So the conversation in which you only "agreed" to "one make out session" is kind of inconsistent with your general view that you both have the right to decide what you do with others. The other view is "he shouldn't be dating when we need time to reconnect after a bad time and when we have small children." You kind of assumed that during the past two years, he wasn't dating because he agreed with this view, and now you're dismayed to find that he didn't.
I think the best outcome here would be to clarify what behaviors you need from him. You've said he's doing some good things and still seems committed; life feels like less of a grind now. At the same time, he's expecting you to play therapist about his new relationship, and he's refusing to slow down when you express discomfort. He's also making last-minute requests for you to handle chores while he does NRE stuff with his new sweetie, which is inconsiderate.
I get why you're upset that they're moving so fast -- you're not getting to enjoy the honeymoon you wanted, and you need more logistical support at home, but a lot of his time and attention is elsewhere. But that's not about how he FEELS; it's about what he DOES. You wanted a honeymoon? What does that mean to you? Taking a trip? Going to concerts or nice dinners more often? Tell him you want that. That he needs to make that happen ASAP, and fit his new relationship around that. More help at home? Tell him specifically what you want him to do -- how much time, how often, what chores. Talk to you about your stuff, the kids, music, instead of his new sweetie? Have some time together that's considered a "date," where he's focused on you and not on his phone with her? Tell him that.
If he agrees to meet your needs, and actually does, then his new relationship will be forced to slow down because he will be making you and the kids a priority, as he should, even if it's not what he feels doing right now.
If he doesn't agree to meet your needs or breaks the agreements, then you'll know you have a partner who, for all his good qualities, is not capable of being a good hinge for you. Now you could consider an ultimatum that if he doesn't agree to mono, you'll leave and find someone who can give you the support you need. Maybe decide you're better off as friends who get together to play or write music, rather than as life partners. For now, although I hear you that you'd prefer the simplicity and clarity of monogamy, it sounds like what you really want is just to have more and better time with your hubby. If he starts handling his NRE better, so that you get those things, you may not find his new love so threatening, and everyone can be happy.