I second the "Buck Island" recommendation. The water is amazing. Renting a car for all or some days depends on how often you and your family like to venture out vs. stay put. Personal preferences. Lots to see all over the island. Cane Bay is a personal favorite spot of mine - west of C-sted. Great snorkeling.

"The cure for anything is saltwater -- sweat, tears, and the sea."

- Isak Dinesen