Hello and welcome to the RTA forums !

It looks like a nice plan for a little sisterly bonding ! If you want to shop and head to Antelope Island on the day of arrival I think you might be better off lodging locally and just get an early start to Yellowstone the following morning. Getting through the airport, collecting the car and getting your bearings all takes time. Can't help with Zip lining or horse riding, but I'm sure you would find somethibg with a search. If you are camping in Yellowstone I would recommend booking sites in advance as it it does fill up in the summer months. You might pick up some info scrolling through the pages of this Yellowstone and Tetons part of a trip report.