Parking is within walking distance, how long depends on the terminal.
Common practice is to dump bags and family at terminal, then go park. Drop off routine will resemble an air terminal with same lack of civility on the part of fellow passengers but far more cooperation on the part of the porters. Be sure to check the room assignment list which they all have to see if you have received a last minute upgrade. They will redo your baggage tags. Tip as if you will never again see your bags if you don't.
Industry standard for pier parking is about $8 a day, pay in advance. Tell the attendant your ship and you will be told the total. Parking is covered but expect a coating of salt when you return. You lock and leave, clubs your option.
It is a given your family will not be where you told them to stay until you catch up.
On return, you can leave family and bags at the curb after clearing customs and go fetch the car but it will seem that each returning passenger has two cars trying to jam into the same space as the busses and vans.
If you can manage, wheel the bags to your car and leave from the parking garage, putting as much space between you and the terminal as possible.
Or - -, pay a porter to bring your bags to your car, depending on how close the garage is and how badly you want to get out of there.
Or - -, possibly the smartest, drag your feet at breakfast, return to room for potty and toothbrush ( a no-no but can be done, depending on rapport with cabin steward), be the last off the ship, pick up only remaining bags and have the baggage pickup area to yourself.
There is a Port of Ft Lauderdale website with maps.