Bahama Passage (1941)

A girl, Carol Delbridge (Madeleine Carroll), whom the audience is quickly informed has been around, and her father arrive to take over the business management of an island in the Bahamas owned by Adrian Ainsworth (Sterling Hayden), descendant of many ancestors who have handled it over the years to the satisfaction of its two hundred and fifty native residents. He is married to a woman who stays away from the island because she is lonely when she's there. Adrian doesn't want Carol or her father there, and they don't want to be either. Romance can't be lurking far behind the beautiful sunset.