Tic,
The best answer for you questions have been stated by Craig123 - you will need to contact your insurance company/broker in the UK and the Jamaican insurance company/broker to determine what is and is not covered. As for a price to be added to a policy in Jamaica or changing the policy to allow tourists to drive the car, my guess is it would be less expensive to rent a car from a legitimate rental company than adding you and all the potential extra drivers to the existing policy.
