Keeping emotion out of sex...thats almost always tougher than it seems.
So you are concerned with her almost being like a child, give an inch, take a mile and continue on while you sit there are watch her bounce around? Thats a tough one because you have to trust in her and really...in the end. The door is open. Some people can only handle so many romantic relationships at once. Others date like fiends. Others are somewhere in between. Would her committing to you and him only quell your fears?
I have broken down in front of her at least five times (and not in front of her twice that many times) and it just pushes her away. And even though I tell myself NOT to ask her to stop
That concerns me. Why is she pushing you away. Is she really or is this something you are seeing through your own glasses? Even at her worst point of NRE she should still be empathetic with your challenges. Pushing you away is like ignoring the problem and moving on hoping you will figure your own shit out. That ignorance of your feelings is a bit of a yellow flag. In my opinion anyways.
There are lots of posts on jealousy, maybe read up on them. Find the root of your jealousy. I think you have nailed part of it - you fear the "will this ever stop" syndrome. If you give over completely how and when will you ever get your needs met. She has already proven to ignore one of those needs.
Also, and others may disagree. If you suffered no jealousy before, it might be something about the new guy throwing you off. Maybe you just don't like him, or maybe there is actually something there you just can't quite get, throwing you into protective mode. Its a true balance between being a good and strong husband and trying to protect you wife vs allowing her her own freedom. Are you concerned by a potential cowboy (man coming in and trying to steal her instead of a true poly relationship) or worse yet, a man taking advantage of her polyness and using her for sex. Not sure either would be correct, but you might be getting a vibe making you defensive.
I haven't really given you any advice, sorry, just babbling. Your post has struck a cord because I usually see it in reverse. As the monogamous person in a poly relationship you have an uphill battle I think (mono on this site, look for his early posts, may be able to shed some light onto it)
Also, Since you seem to also be the stay at home dad, I would be concerned with potential dependency issues which may or may not be the case. But if you are stuck (and I use that word purposefully) at home with the kids while she gets to play, that creates potential resentmnet. Why not find a babysitter? I realize this costs money, but at these early stages it could be very difficult to be at home, while she is having her fun.
Best of luck