Sorry you're having to go through this. You can't control what your sister does. I know, I've been there before and ended up with one of my sisters dogs, I can't believe we're even related! I hope you can take the dog and either keep her or at least foster her until she finds the home she deserves.
If I may make a suggestion, please try to channel your anger into just being concerned for getting the dog a home and worry about your sister later. As for the visiting relatives, ignore what they say and start counting the days until they go home. I wish you the best of luck in helping this pup.{hugs}