ok, i'll bite...what's a cowgirl?
i don't think you have to just 'accept it the way it is'. any relationship should include communication with all parties being free to express their opinions and needs to the others. Part of the issue here, imo, is the way you are expressing your needs. Histrionics and demanding he leave his family really isn't, imo, fair. It's not like you got to that country and then he told you 'oh, btw, i have a wife and kids'.
Being a member of a poly family doesn't give anyone license to be a (for want of a better word) 'homewrecker'. Maybe this really isn't the lifestyle for you. It's difficult, even when you're in the catbird seat-as a hinge, it is my job to help faciliate smooth and happy relationships and harmony within our family. Hard enough to do with one partner, much less with multiples.
You Do need to find peace and happiness from within you-no other person can make you happy if you are not. But there IS happiness that comes from our surroundings and the people with whom we live. But I think you have to give happiness...compromise...and sometimes, yes, just suck it up...to your significant others-him and her. Family time is important to their children. Dinner together is also important to you so there has to be some compromise there. Maybe he eats dinner with you 2 nights a week and you don't complain the other 5. Maybe you pack him a lunch and picnic with him a couple times a week. You can put on your thinking cap and figure something out.
It is my experience that when you give someone an ultimatum, they almost never choose the option YOU want them to...and if they do, it doesn't last for long. Nobody likes to be pushed.