HSR,
In response to your most recent questions, my suggestion would be to drop Sorrento / Naples / Pompeii / Herculaneum / Vesuvius from this trip. Given the fact that the majority of places you want to visit are Rome and north, I'd focus on that area this time. As the trip is so short, it will be important to minimize travel times so that you have as much time for sightseeing as possible.
Using a car for visiting "Naples and Pompeii or Herculaneum and Vesuvius" wouldn't be my first choice. The traffic in Naples is horrendous, and traffic in Sorrento also seemed a bit "chaotic" and busy. I don't have any information on parking in Sorrento.
Note that for driving in Italy, a compulsory International Driver's Permit will be required, which must be used in conjunction with your regular D.L. You'd also have to be very careful to avoid any Zona Traffico Limitato areas, which come with a hefty fine EACH time drivers pass through one of the automated Cameras. I've seen these in the south also, so they're certainly not limited only to Florence.
Which towns do you require lodging suggestions for? Could you provide some "guidelines" on what type of accommodations you prefer and the price range? I'm sure the group here will have lots of good suggestions.
Cheers!