I agree to just be honest and say that Claire isn't welcome in your home, citing the liklihood she wouldn't want to come anyway seeing as how she made it clear she has no affinity for you.
I love hosting and having parties and having people in my home. I am happy to welcome relatives and friends of friends. I have a very "open" policy. However, there are certain people who are not welcome in my home for various reasons. Period. No exceptions. And I have no trouble saying so. And I have.
So as an example, a friend of mine brought a friend of hers to a party I gave (with advance approval of course) and the friend proceeded to behave in ways that just didn't work for me. She was generally rude and inappropriate. My friend wanted to invite her again to a subsequent party and I said sorry, but I didn't like how she behaved and wouldn't feel comfortable hosting her again.
No biggie. Friend accepted that. We're still good friends, years later. She understood. And believe me, what this woman did was no where near as agregious as what you described because her behavior wasn't personal, just inappropriate.
Just say no.