Hi Virginia! My husband and I went solo last summer to "check it out" for our family of 5 with three girls.... 11, 9, and 5. We fell in love with the island and are booked for the last week in May. The variety of activities won me over for the kids.... and the beauty and beach for my my husband and I. We went through each day... and each activity asking ourselves... what would the kids think (or be doing). Not to mention (like you said) I felt very safe the whole time, and I never felt (like in some places I've traveled) that there is resentment to tourists.
We started snorkeling along hike/beach closest to Cruz Bay... I think its' called Lindt Point Trail and Solomon Beach. It was beautiful but wasn't convinced it was for the kids. Then went to Honeymoon beach and continued to work our way west along the north shore beaches. Trunk Bay and Maho Beach won me over for the kids. The variety of coral and sea life was amazing.... huge turtles at Maho and fish at Trunk.
I think that my kids will also love the hiking trails (cool cactus, crabs, mongoose). There aren't many places that I saw that have the same feel as a luxury or all-inclusive where you sit and recline in a lounge chair and order drinks (which concerned me at first). However, we're excited about venturing out and trying something new with our kids. I think the pay-off for not having that is that you see more sea life, coral, and quiet beaches.
My husband and I traveled to the Baths one day and, and I think my kids would love spending one day there. We are staying in a villa with a pool (which I know my kids will love).
Good luck on your decision!