I hate feeling anxious and out of control but I think I hate it a bit more feeling like other people may be disappointed in me or think less of me, and if I don't like the person, that they may have gotten the better of me. When all else fails, I take out my minimalist, black-and-white thinking

and use logic to control where my anxious feelings are failing.
It's a party. Ask yourself if you want to be afraid of a party, a celebration. The woman is going to be "family" after everyone is married and so you'll probably have to "tolerate" her and see her a bit in the next 20-50 years if you stay married to her brother and the creeks don't rise. I would go and stand around glaring at people, daring them to include me :-) But I'd keep the moral superiority stance of having at least shown up -- one can lead a horse to water but not make her drink; one can lead me to a bachelorette party but you can't make me dance.
I've gone to a lot of events I really really didn't want to go to but I can't think of one where the situation didn't turn out better than I expected it to.