The inside areas are all air conditioned and pretty cool. I was cold in my formal gown and had to go outside (at night, mind you) to warm up! Wearing clothes inside is needed just to keep from shivering if nothing else. OK, on a serious note... yes I would have felt odd shopping in Mickeys Mates in just a swimsuit. I did see plenty of people (including me) going from deck to rooms in just swimsuits though, and that was just fine.
Cover-ups vary in ... coverage, as well. I love the look of those wispy scarves that match the suit and tie around the waist, but I wouldn't consider it as qualifying as dressed.
Tell your sister-in-law that a throw-over dress will go far. I ended up wearing a crumply-fabric tropical dress over the suit a few times (great at CC) and was glad I'd packed it. No wrinkles to care about, & it took little space.
Have fun!