While the title you mentioned, "A Storm In Jamaica," sounds similar, it's actually the title of a 1958 novel by Daphne du Maurier. The story was adapted for a 1965 film, but it did not feature Rock Hudson.
Here's a brief summary of "The Storm" (1956):
* Plot: The film follows a young school teacher (Hudson) who is stranded on a remote island during a hurricane with a group of schoolchildren.
* Director: Daniel Mann
* Other notable actors: Dorothy McGuire, Diana Sands, and Philip Carey
It's possible that you might have misremembered the title, or perhaps the film left a strong impression on you, making you recall it vividly. However, "The Storm" is the movie that best matches your description.