Thanks Chuck. I want my family to see and experience historically significant sites ie.the Colosseum, Pantheon, The Vatican, the Trevi Fountain, Piazza Navona, and possibly the Villa Borghese. We would be there the Friday morning before Easter Week and staying near Rome for a couple of days and then moving close to Lucca, Siena, or San Gimignano for the remainder of the trip and doing day trips. I don't know if there is public transportation to help getting around Tuscany, hence the rental cars. My understanding is that the flights and agrituristas are often discounted at that time of year. Because of time constraints, the trip has to be limited in scope.
By any chance is the first of your two days in Rome your arrival day? Because, if so, you will miss a good part of the day getting through and from the airport to your hotel, even if you arrive quite early, and the likelihood is good that at least some members of your party are going to be jet-lagged enough that they won't be up for the kind of heavy sightseeing involved in getting to all the sights on your list. If you have three nights and two full days in Rome, it's doable, but if you only have one full day and a jet-lagged half day, you're likely to find it a miserable slog.
It depends somewhat on where you want to go in the Tuscan countryside whether public transportation is convenient, but in general, a car is very nice to have and opens up a lot of options you won't have if you're limited to buses and trains. Lucca is easy by train from Florence. Siena is convenient by bus or train from Florence (bus is better because the bus station is located closer to the historic quarter of the city), and you can reach San Gimignano from Siena by bus, although I think you have to change in maybe Empoli. With a car, though, you could venture into the Val d'Orcia, the area around Montepulciano, Montalcino and Pienza. Google them and see what you think. This area is not accessible by public transport.