I can tell you how I would do it given what you want to see:
I would pick up the car in Venice. I would stay outside of Florence in the hills of Chianti. (We did this in 2008. had a beautiful 2 bedroom, one bath apartment with a kitchen and a washing machine for 115 euros for 4 people. The apartment was about 1200 square feet-huge, and was part of working vineyard.) I would use public transportation to get into Florence (we could walk to the bus and ride in) and use the car to day trip to Pisa, Siens San G, Cortona, wherever you wanted to go. Then I would drive to Orvieto or Orte. I would go via Assisi. I would drop the car in Orvieto or Orte and take the train from into Rome.
We drove in Florence once and will never do it again. It is possible to drive there, but it is not fun and was stressful. Be sure you research ZTL zones and traffic cameras in these areas. Traffic cameras are everywhere, not just on major highways. And ZTL zones are in most cities with old towns. We always went the speed limit, and we were very careful to watch for the ZTL signs in cities. We never got a ticket (2 years later, knock on wood)
The only reason I would stay in Pisa and day trip from there was if I wanted to try to have day on the Cinque Terre. However, you are farther from many of the more interesting sites in the Tuscany area-long driving for day trips. The CT is worth a night or two, but you will have to plot out what all you want to see before you will know if you can squeeze it in this trip. We did this trip with my sister and her husband in 2008. We did 2 nights CT, 3 nights agritourismo in Tuscany, 3 nights Rome, 3 nights Venice. We day tripped to Florence, Siena, Pisa, Orvieto and Assisi. It was their first trip, and it worked really well. They got to see most of their "must sees" and a lot of their "would be nice". Our time in the Vineyards of Tuscany was heavenly.