My question is this: is it common in polyamorous relationships for someone to quickly fall in love with another to the degree that they wish to leave a long-time relationship? And how is that poly, if one replaces another?
I think that is a side issue. It's not about whether or not he's really polyamorous or not. It's about what you both want from THIS relationship and what shape you want it to be next. Don't distract yourself with "Why can't it be thus?" or "Why isn't it thus?"
Focus on what IS here.
Set his name aside for a moment.
In general, do you feel you need to be connected to a legal husband person as friends AND lovers?
If so, your current DH is not longer that man then. That much is clear and has been clear.
A new person cannot come in to fill the legal husband role if he's still holding on to it. Best for him to vacate that place and for you both to agree to be co-parents and friends and good exes instead. Whether you live together for a while or not -- that's another thing. But start sorting yourselves out here.
What is love to you? Do you subscribe to triangular love theory?
If so? Even if consummate love as run it's course on this one? It doesn't mean you cannot keep loving in another form.
Right now since he's trying to share inner life feelings kinda... hodge podge up and down? And I'm not getting that you have shared with him about the cheating and you feel your own up and down?
I'm not sure how much real emotional intimacy or mind intimacy you have been sharing. You are clear that you do not share body intimacy.
So if you guys are parked in "empty love" right now where's it just the marriage committment to be together that is holding you together? It feels flat? To me it seems like progress/deepening relationship to just end the marriage. End the conjugal duties. Not just to free up "legal spouse" slots for some future happiness to come along to fill with less brouhaha.
But to open up to loving each other in mind/heart intimacy and really BE good friends who are committed to the raising of the child in a positive way. That I think you can both get behind. Or sound like you could. I'm not sure either one is really behind holding up marriage vows that don't mean anything any more.
Platonic companionate love is more connected than empty love alone.
To me getting back into right relationship with each other (even if it means changing relationship shape) IS loving behavior and it is progress than keeping the unsatisfying status quo. You will both process loss of the marraige, but hopefully can move it to embracing a new thing. You may need time apart before you can be together again as friends and coparents. You may need pro counseling support in the transition. I cannot predict what you may need.
You guys need to talk and sort yourselves out on this. What each is and is not willing to do. DIRECTLY. Rather than avoiding facing the state of the relationship and doing things like having affairs or suggesting Opening Up to polyamory from a broken relationship place rather than a health one.
Land THIS relationship well and bring it back down to Earth well before launching new ones. Even new ones with each other. (ex: friends and coparents)
I dunno if that helps. I'm sorry you are down today.