Just go through with an open mind, be your best self and let the chips fall where they may. Ultimately, any group who picks you will be choosing YOU. It's very neat if it works out to be a legacy chapter for you -- either with your grandmother, etc. or your sister, et al. Heck, you might even select a third option and start your own tradition!
Whatever happens, promise us you will come back and tell us how it worked out. That's the least you can do for all of this good (free) advice!