I think you are entirely reasonable in feeling excluded and hurt.
You are the only SIL to be excluded from the wedding party. They have all kept your being excluded a secret, until MIL accidentally let slip.
Now she has let the secret out, she can't or won't explain why SIL has chosen to leave you out and include all the others.
You say that the family is usually close and socialise with each other a lot, yet she's chosen to leave just you out and none of the others have breathed a word.
You are now wondering how often they are meeting without you and chatting online in groups you are not part of, which has made you wonder if you are not as close to any of them as you thought you were.
And you're probably going to have to sit through the family get togethers while they talk about the exciting plans for days out trying dresses etc that they have excluded you from.
Your DP is hurt as well.
And it's likely that some bigmouth in the family will get pissed at the wedding and want to know why you're the only SIL not part of the bridal party, but they'll ask you rather than the Bride.
The only option for you now is to book your wedding for the week before hers and steal every bit of thunder she's got. You could also invite all the other SILs to be your bridesmaids and ask if they can wear the bridesmaids dresses to both weddings to save on costs, leaving the Bride out of course because she can't wear her wedding dress to be a bridesmaid can she 
Seriously, I think all you can do is take a dignified step back and let them get on with it and hope they are not crass enough to start making plans for days out trying dresses or getting hair and make-up done etc in front of you now MIL has spilled the beans.