Hi Laurie and welcome to UKY. I would think that the Caribbean's proximity to the US makes it an ideal location for offshore American weddings, so they would have published info as to the legal requirements and validity.
Also, I think you'd up your chances of having the marriage recognized by the UK if you getting married in a Commonwealth country or UK territory.
In any case, I can't imagine that a marriage in the Caribbean wouldn't be considered "valid" by the US or UK, but rather that you'd need additional documentation. For example, I know that Italy doesn't recognize marriage certificates issued in the USA, unless they're accompanied by an apostille from the US Department of State, which is easy enough to get.
Good luck whatever you decide!