I totally, TOTALLY understand about wanting to have something that is yours and that your best friend doesn't do with you.
She might not have to bad mouth her friend, the sisters might dislike her all on their own.
OK I'm being a little flip, but the important thing for everyone to know is just because it's your sister's sorority, she can't necessarily "get someone in." Trust me, the other sisters will figure out if the friend just wants to be in because of your sister, and unless they are hurting for numbers it likely won't go over.