Ken, my son has AS. He is 11 and despises, like all the rest of us, going to my wife's grandmother for Christmas. My wife hates it. The cousins she grew up with hate it. There isn't a single person in that house, other than grandmother and the few of the under-5 set, that actually want to be there. Torture. Everyone gets there, says hi and looks at the door wondering when they can slip out. Worse yet, no beer is served (kidding but true).
I don't know how much of your problem is AS related and how much is the realization that this is an utter, complete waste of time. We are sold on the idea that Christmas is about "the family"... how many of us can honesty say that we love being with our extended families -- cousins, nieces and whoever that we have nothing in common with.
You sound as though you are a teenager, although you didn't give your age; you are old enough now to say to your parents that you are uncomfortable going, that you are suffering anxiety at the very thought of it, and that you'd be more than happy to visit your grandmother another time all alone. Part of growing up is exerting your authority. Just say no.
Speaking for me, I stopped going after 15 years of it. I am staying home with my dog.