Wow, I really feel for you.
"I have been reluctant to be close to him or spend much time with him lately. He has been jealous of my other relationship, and I wonder if he's trying to get back at me in some way"
That is scary to me. I have seen many relationships go sour very quickly when this type of dynamic takes root. I would nip it in the bud strongly or fear that it grow very big very quickly and be harder to remedy later.
There is nothing wrong with vetoing her. They broke a core rule. She is causing your primary relationship trouble. That is what a veto is for. If you can't use it when you need to use it then it's no good bothering to talk about even the concept of being able to veto.
I would say to use it. Veto her. See where his head and priorities are. It will clarify things for you. Not fun, but not worse than the mire you are trudging through right now.
For what it's worth and nothing more.