She's your friend.
When someone is a friend this would have come up in several conversations. Like
"Hey, kiddo is asking me about having a party at that Medieval place but he wants only boys to come, how would female twin kiddo feel about that. We sure don't want her to feel left out so why don't we do an all girls day starting at Clair's and ending with XXXXX".
"Hi, I have an idea! Kiddo wants an only boy party this year at that Medieval place. What do you think I should do? This is the first year we'd be splitting the kids up and I feel really sad about this. Is it okay to let him do this? I keep thinking about how (your female twin kiddo) is going to feel and I want to tell him no. This is hard! How would you handle this?"
By talking to her well before about the situation, which is what we do with friends, gives her the chance to prepare her girl and give you feedback. You can always say no to your kiddo. Truth is, you're paying for it and understand the hurt and pain behind a rejection. Even though that's not what it is the girl will likely feel rejected and left out.
I think everyone going and then splitting up would be good. IF IF IF the mom is okay with that. I mean, she doesn't want her girl to be the only one not included. Or just her and her cousin.
It's a tough one, I hope it works out.
BTW, how old is he?
If he's getting 7 or 8 it's time for the kids to have separate parties. I think 1st grade is it as far as boy girl parties. After that you're going to see more and more of them just wanting a few close friends and not the whole class or joint parties.