Phew! A lot of complexity, you're right.
I have no answers. None. Zip. Nada.
You seem relationship-oriented and he seems to have a side that is fascinated by casual sex. Is that the fundamental issue?
How does the partner you've been with for 10 years deal with this? Is he OK with the flirting and attempted hookups, or is he feeling uncomfortable too? Does he think you're being controlling, or does he think your feelings are justified?
It's important in relationships, and poly ones especially, to see that each person is getting most of their needs met. It's important to cultivate the sense of compersion, feeling happiness when you know or imagine a loved one is happy or pleased. (It's the feeling that one gets when one knows one's lover is getting all sexed up and happy with someone else -- "I'm so glad she's feeling good right now, it makes me feel all tingly for her.") And it's important in all relationships not to be a doormat! How those dynamics are playing out in your relationship I can't say. But you might think about it.