My opinion may be very unpopular around here, but I think your daughter is being rude.
She is 14 years old- old enough to understand that there are some things that she should do in spite of the fact that she doesn't want to.
Eat your vegetables, go to the dentist- we do these things to stay healthy.
Hold open a door for other people, say please and thank you, pose for pictures when it means a lot to your mom- we do these things to be kind and polite and generous.
I don't think its unreasonable to ask or require her to pose for a limited number of pictures 2-3 times a year (like a PP said- maybe Christmas, birthday, back to school). There's a safety issue too. If she refuses, then I would refuse to do something "optional" for her that she expects / enjoys.
The only mystery part of this question is the fact that you think she may be on the autism spectrum. I'm not sure if that fact should affect your expectations of her.
A PP's suggestion of giving her a way to "hide" in the pictures struck me as a fun and possible way to get her in (I had actually pictured your DD holding up a "censored" sign over her face or a black dot or something, but a book would be fun too).
I do generally think she should just suck it up though (unless it is really not medically/mentally possible for her). But if she won't/can't come around if you discuss your wants with her, then a fun way to include her in the picture without her face would work. Maybe get her to peek through her hand? Or do a "cousin IT" kind of thing with her hair.