There’s no one you absolutely have to invite to your wedding, well, aside from your spouse-to-be, the odd witness and, of course, an officiant of sorts to make it all official. 🙂
On a more serious note, aside from these three parties, in theory, there is nobody you MUST invite to your big day though, in practice, there will be a bunch of people you simply couldn’t get away with not inviting.
Though your sister appears to fit squarely on the list of those you don’t have to (or want to) invite, remember that though she may be in your bad books at present, there’s nothing to say that you both won’t reconnect down the track, at which time you’ll likely both regret the fact that she wasn’t at your wedding.
As long as her presence won’t cast too dark a pall over your wedding day, ask yourself if there’s any harm in having her there as you (and she) may one day bitterly regret the decision not to invite her. Of course, I’m not privvy to your history with your sister, so, to my mind, inviting her is by far the wisest option because it is aimed at protecting both your hearts in the long-term and avoiding a lifelong regret.
If, however, you’re sure you won’t be able to make it through what should be a very happy day without some bad feeling between you and her – or suspect your big day may be ruined by her presence, then you may be best not inviting her.
Just think long and hard before making a final decision.