If you are living at your mother's home and your sister comes, I would go out, go somewhere else and let your sister and mother get together on their own. Presumably your sister came to your mother's house to see your mother, not you.

I would make sure I "don't have room" for guests where you move. Apparently she doesn't go visit your mother much, why should you have your sister (or anyone else) come visit you if you don't like? And if it is 15 minutes from where everyone else lives; they can visit the city, anytime they want but you're sorry, you're not available.

Siblings are like parents and don't get chosen by us; we might love them but we're not required to like them, they have their own personalities, interests, and their portion of sibling rivalry, everyone thinking they have to vie for their parents' attention. Look at a group of puppies; they're all over the mother trying to get the best teat and often the runt doesn't get enough. I would try to feel sorry for your sister; you're the youngest, the baby, and she's probably jealous.

You're 27, it's time to give up the rivalry for your mother's attention, live your own life and let your sister do her thing however she chooses. The "she started it" thing doesn't fly with anyone else out in the outside world, doesn't help you because no one else cares anywhere else, they have their own family dynamics. Do your thing and fly away from the nest.