Since you are of legal age, you can have the car transfered into your name and a new insurance policy in your name.
You will be required to carry PIP and Liability in the State of Florida. Once the car and insurance are all in your name there is no problem.
For Example if you are renting a room from someone in their home, they would not have the liability for your car. It is the same situation you may be living in the Family house, but the car is yours and the insurance is yours. You have the responsibility for the payment of the insurance, car, repairs and gas, so the liability falls on you.
I am very familiar with this since my son will be turning 18 and going to College. He will be living at home, but his car and insurance will all be put into his name. We will not be liable, as it is all his responsibility because he will be of legal age.
This is the Fl. Law for auto insurance: http://www.flhsmv.gov/ddl/frfaqgen.html
I hope this helps. Joan