Rome to Florence to Sorrento to Rome.

You can't drive into central Florence and you don't want to drive along the Amalfi Coast in season.

Even if you could, why wasting vacation time on a car, driving along a boring motorway when trains run from central Rome to central Florence at 300 kmh? If you want to roam around rural Tuscany, pick a car in Florence and head south towards Rome. Driving out of Florence without being fined is possible.

If you are flying into FCO, there are direct high speed trains departing from the airport station to Florence SM Novella at 11:08 am
and 15:08. At different times a transfer in Rome is always needed.

Renting a car isn't always the easiest or best way to get around Italy. Train service is so affordable, reliable and comfortable and quicker than driving. May I suggest when you get to Naples (that's the end of the Freccia line), you consider taking the ferry over to Sorrento? Schedules may not coincide but if they do I would certainly do it. Even if they don't I'd still do it. There's places to see, sit, eat right at the port. The trip across the bay is faster than the local train and certainly gives better views of the shore and Capri. The view of Sorrento as you get closer is beautiful. For me, that makes that part of the trip part of the vacation. 3 nights in Sorrento? That's 2 days. You can take one of those days to do the Amalfi Coast (I like taking the ferry from Sorrento and the bus back from Amalfi town). That leaves you 1 day for whatever else you want to do. The nice thing, among lots of nice things, about Sorrento is that the evening hours can be wonderful. It's a wonderful place to meander around and enjoy the shops, views, restaurants and lots of things made with lemon. Enjoy!

In Florence I'd like to suggest you take in the Duomo museum. It just reopened 2 years ago. I'm not a museum person and, truth be told, Florence is not my favorite place in Italy, but this is one museum I got out of my way to visit. I've done all the rest over the years - this one I plan my train schedule to allow me a few hours in this very interesting place. That and lunch at the Mercato Centrale makes me very happy.

You don't have a lot of time in Rome. I'd suggest make your 'must see' list and not be afraid to cross things off it. You never know what will catch your attention. I've learned two things about Rome: 1) if you get tired of one century all you have to do is turn at the next corner - there's a different century right there; and 2) Rome's been there for thousands of years - it'll be there when you return! And I'm sure you will want to return!