St. Maarten/St. Martin has a number of family-friendly resorts and restaurants featuring kids' menus. Anguilla is very family-friendly, particularly during spring break, the shoulder seasons, and summer; the calm, clear waters are perfect for beginning swimmers. The Malliouhana resort, on Anguilla, has a wonderful children's playground (with a pirate ship) that's separate from the main section of the resort. Although a number of St. Barts resorts discourage children during high season, it's quite a kid-friendly place the rest of the year.
Even those hotels and resorts with specific adults-only aspects offer some sort of kid-friendly amenities and programs. Many of the beaches are particularly attractive for families with toddlers and young children, and older kids will have plenty of nonmotorized watersports activities (snorkeling, sailing, parasailing) to keep them happy.