Welcome to PPRuNe Marc,
I don't have local knowledge of rental possibilities in the South Florida area, so hopefully someone will be along with some wisdom for you on that. I have flown my Cessna across to the Bahamas once, and up and down the Florida Keys many times. they are both flights well worth making. Taking 4 adults and baggage in a 182 may be asking a little much of the airplane in the warm summer temperatures, so factor that into your expectations.
Good luck!