To go with what Chief said: If it's not around the trunk, check the umbrella structure to see if it's there.
If not, like Chief asked, can you go back to a saved game and try again? Only this time, after you pull the plug from the trunk and before you take the key, go to the umbrella structure and do what you have to do there. Then go back to the lighthouse and take the key from the trunk.
Wouldn't that jar your mustard!