I work for a US coroporation and my territory is the Eastern Caribbean.
Your children are going to have a blast as the countries you are visiting offer a wide variety of places to have a great time.
My absolute favorite is St. Lucia. Don't miss the Pitons - beautiful volcanos. Hike the rainforest and visit the sulfer springs. The photographs you can take on that side of the island are spectacular. There are katmaran sail tours that re so much fun for all ages as well.
Great dining in Rodney Bay in St. Lucia and lots of night life too!
You will not find nudity or toplessness in St. LUcia - it's a very catholic country.
St. Maarten has some of the best restaurants and shopping in the Caribbean. They also offer SNUBA which is a safe and easy way to learn to scubadive in a controlled environment. Kids will love that. Stay away from Orient beach to avoid the nudity.
Barbados is huge with great great beaches and depending on the night you are there - dance clubs right on the beach which your teens will love.
Antigua is very rural and rustic with lots of cows and sheep in the roads. Also gorgeous beaches but topless is allowed on many of them.
Hope this helps. Have a great time!