The Keyhole (1933)

Anne Brooks is being blackmailed by her old dancing partner Maurice. They married when she was young but broke up after which he said he was getting a quickie divorce. Anne married the much older millionaire Schuyler Brooks only to have Maurice return to reveal he didn't obtain the divorce after all. Now he wants money to keep quiet. Anne reveals her secret to Schuyler's sister Portia who devises a scheme to trick Maurice into leaving the country by having Anne suddenly travel alone to Cuba. Once out of the country Portia will use her influence to block Maurice's return. However, Anne's request for a vacation by herself in Cuba arouses Schuyler's already simmering jealousy. He hires detective Neil Davis to follow her and prove whether or not she is faithful. Neil is unsuccessful in seducing Anne, then realizes he is falling in love with her.