Hi wvsunflower, welcome to Cruise-Chat. Half Moon Cay is a private island and a beautiful beach day. It's one of my favorite private islands. St. Thomas is great for shopping, snorkeling, and sight-seeing. With 2 ladies in their 70s, I recommend staying on the island. Normally, I would say grab the ferry and go to St. John then grab a cab to Trunk Bay. There are some nice beaches on St. Thomas, though. Coki Beach or Magen's Bay would be good for your mom and aunt. They have all the necessary ammenities. There is great shopping near the port, if you dock in Havensight you'll be closer to town. Grand Turk, I'd highly recommend snorkeling for you and your cousin. The hurricane pretty much wiped out the island, but you could take a tour. There is a shopping area right at the pier and a nice beach there. In San Juan, a tour of Old San Juan or a visit to the Bacardi Factory would be nice for all.
Hope you have a wonderful cruise! Bon Voyage