When we take the kids to the Caribbean, we usually stay at an all-inclusive place. I like Windjammer Landing and Coconut Bay in St. Lucia, and Beaches in Turks and Caicos. Windjammer Landing is definitely more oriented to teens and older than to small children, though.
That said, I've felt safer in St. Lucia than Mexico or Jamaica.
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Opinions are strictly my own, and have nothing to do with my employer.