OP I think you're getting a hard time on here.
If someone is an introvert, and finds social situations awkward and uncomfortable, why are they the ones who are expected to change their personality to fit in with others' ideas of what is acceptable? Why should OP be forced to go on holiday if she doesn't want to? Why is is OK for the sister to be trying to mould OP into something that she isn't? Why doesn't she (the bride) do the sisterly thing and accept her sister for what she is?
Starlight, you say about your sister "however I really do wish she actually made an effort sometimes and pretended to care even if she didn't..* Why does she have to pretend to care to fit your wishes?
What's coming across in this thread is that conformity is expected, and it's OK to pressure someone if they don't, even if they're not harming anyone else. And I'm not writing this because I'm an introvert myself, far from it.
However, OP I think you should go, because I think this is one of those occasions where it is potentially harming others. The rift could spread much wider than just you and your sister. But go as yourself. Ignore her comments about the hairdressers - a hairstyle isn't going to turn you into an extrovert. And don't go jogging with her and do a city break if you don't want to, she doesn't have the right to turn you into someone you aren't just because it would suit her better. Then when the wedding's over, maybe you could manage to talk to her, even if you feel you're not very good at it, and try to work towards each of you accepting the other as you are.