We always rent a car but...

Florence, Venice, Milan, Rome "free parking options". I wonder where you heard that? It's never easier to have a car while you stay in big cities and tour. Venice is NEVER a good place for a rental car which will ALWAYS stay parked in the big parking garages at the end of the causeway - and they are NOT free.

Dolomites, Tuscany - fine for rental cars.

It sounds like you're not locked into Milan, so I would fly to Venice first and pick up the car upon departing. Do all your small town visiting and drop the car upon arrival in Florence. Then the last leg can be a fast train to Rome.

Fly to VCE.
Stay in Venice without a car (for a number of nights as you see fit, but 3 nights for Venice would be good if you have the time)
Rent car upon leaving Venice. All rental car companies are on Piazzale Roma (presumably where the bus or taxi from the airport dropped you off when you arrived).
With the car you should go to the following locations:
DOLOMITES
LAKE GARDA
TUSCANY (see note (*) below for Florence)
UMBRIA.
Then ROME, where you'd drop the car upon arrival.
Fly out of Rome Fiumicino airport (FCO)

(*)Florence is the capital city of Tuscany and is located in Northern Tuscany. Florence is not a good place to have a car but since you need it to visit further down in Umbria, you should look for a place outside of Florence, or outside the city center of Florence, where a car can be taken. As you know, the historical city center of Florence is forbidden to cars, except for residents with permit, therefore you'll have to keep it parked at the hotel (outside the city center) while you tour the city. A good option is to find a place in the countryside outside of Florence (or a smaller town) and commute to Florence during the day to visit it by either car or public transportation (if available). If you commute in by car, you will need to park the car at the parking lots outside the city center (there are several).

Roberto has the plan...
I have rented like this a number of times and you are right, it is easier to just get your car and keep the same one, also, it is often cheaper for the longer rental period. Should be no drop fee as you are picking up and dropping in Italy. Even though you might pay a bit for parking it will still probably be a savings to keeps the same car. In Florence I have had a car a few times and I think I stayed at a Holiday Inn that was quite near the airport but out of the city center. They had parking as well as a shuttle into the city center. It was really easy to deal with.

I travel by car most of the time and I enjoy the freedom and spontaneity that it gives me. I have found so many amazing places on my own simply by taking an interesting little turn n the road. I am ok moving around a bit as it is not that difficult with a car. If I don't find a hotel in one village, I drive on to the next. Big cities, I would make reservations, as you want to be sure they have parking, but if you are comfortable with a more free itinerary, then a road trip in Italy is amazing.

You could also leave Florence as your last place to see in Tuscany and drop the car at the airport before you stay in Florence, then take the train to Rome. It would probably mean a bit of backtracking, but it would have you not worrying about the car in Florence, and less time paying for rental.

we have leased a car a couple of times, which works well for us, as we need it for a long trip. BUT we deliberately try and find ways to not have to park in the big cities. In florence for example we stayed in fiesole, a lovely small town a short bus ride away looking down on florence. we parked with no problem and just caught the local bus into florence. it felt 'special' using the local bus to get around and saved lots of problems. including when we left we didn't have to drive out of a busy city. also we got to look around a nice small town and the large city in the one visit. our hosts have always given us great directions to catch the local transport and dinner options.

In Venice we did the same thing. we stayed at Jesolo and caught the local bus and a ferry across to the islands and venice itself. so we got to see Venice from the water and got to stay in another interesting town as well.
At lake como the car was not a problem.
We don't care if we don't use the car each day, or if it sits idle for a few days.( we factor the cost into the trip, and the time it saves us) while it would not suit everyone, this type of travel has given us the best of both worlds. the flexibility of having a car to use all the time but planning the trip so we don't have the hassle of parking etc in large cities and finding lovely small towns to stay in.
hope this helps.