http://answers.yahoo.com/question/index?qid=20131129171852AA0K7zV
If you cannot go without making trouble, then don't.
None of the arrangements are up to you, and it is not up to the bride to pay your way. If you are able to pay to go on vacation with your GF, then it makes one wonder why you wouldn't be able to go to your own sister's wedding.
It doesn't matter why anyone else didn't go - I have gone to every wedding to which i have been invited, because it is an honor to be included. Even the wedding I knew for a fact would end badly, and soon, was attended in formal attire and a gift given.
Perhaps the best gift you could offer would be your absence.
Send a nice card wishing your sister and her husband every possible happiness, and then do whatever you want with your day. From the sounds of it, that could be what she really was hoping for in the first place.