Driving from Florence to Cinque Terre/Siena

The last thing I would want to deal with in Cinque Terre is a car. There is no parking in the towns and the parking areas are small, outside of town and usually very curvy and hilly to navigate on foot with luggage. Have you considered picking up your vehicle in La Spezia after leaving Cinque Terre? The train from Florence to Cinque Terre is very easy and the train to Venice is also easy. We spent a month in Italy last September and never rented a car. It was easy and stress free!

I don't see any reason in your itinerary to have a rental car at all.
Florence to Siena: easier by bus then car
Florence to Cinque Terre: easier by train than car
Cinque Terre to Venice or Verona: easier by train than car

Sounds like you are making quick trips, which means highways. Highways in Italy are no more romantic or beautiful than highways in the US ; they are eyesores all over the world. Actually in Italy given the number of toll booths and automatic speed cameras I would say they are even less beautiful.

Now, if you were staying much longer, exploring the countryside, staying outside of towns, taking longer scenic roads to your destinations that would be different.

I agree with mreynolds. Unless you are making side trips somewhere, you don't need a car for your itinerary.

On my trips to Italy I've only rented cars while in Tuscany. Otherwise it is a disadvantage to have one. I've been to all the places on your itinerary and would not want a car in any of them. Trains in Italy are the way to go. The exception would be the bus between Siena and Florence. It will take you from city center to city center.

I drove pretty much all of that, it was super easy. We stayed in Montecatini Terme not far from Florence. For CT we drove to La Spezia and parked at train station, took train into CT.

As others have mentioned, the train would work for all of your stops. Driving to Sienna was beautiful though, so I understand the appeal.

Siena- drive and park near top of hill. More flexibility than taking a bus. Only negative is parking fee in center of Florence for one night. Perhaps your hotel can suggest a garage.
Cinque Terre- We left our car for two nights in a large lot in Monterosso. Easy. Driving down to the coast wasn't bad at all.

For your itinerary - no car. Day trip to Siena from Florence - bus. Car would be a useless expense. From Florence to Cinque Terre - train. Car would be a big mistake. I know because I did it. To Vernazza. Narrow winding road. Everywhere else it would be one way, not there. If you meet a car in a wrong spot - too bad. One of you is backing for considerable distance. God forbid that other cars will appear. And then you come to the edge of the town; there is a small parking lot and it's full. So turn around, drive up to find little spot somewhere by the road. If you are not very lucky it could be few kilometers up. And then walk down to the town and ultimately
back to the car. Train is so much easier.

Do you already know about camera controlled ZTL areas, where only residents can drive in?