my husband says he wants to be certain the see the history. It's everywhere. Take the Doge's Palace Secret Itineraries tour in Venice. For more insight, take a guided tour of the Colosseum and Forum in Rome.
this is our first trip to Europe. . . A new thought that we are considering is taking the train all the way from Venice to Rome or Naples and the backtracking on our own from there. The thought is that is would give us a bit of time to get over jet lag (affects my husband more) and get a general feel of the countryside. Driving and jetlag are a terrible combination. It's like combining driving and alcohol. Venice is the best place to relax for 2-3 days and soak it up while getting over jetlag. And you may not need a car at all. Most towns that you will want to see have turned their historic centers into ZTL areas, where private cars are not allowed. The signs are not always spotted by drivers who are concentrating on the unfamiliar car, narrow, winding streets, traffic signals, and other distractions. The fines are automatic (cameras/radar) and hundreds of euros. Parking can be a nightmare. You can easily visit Tuscan towns by bus/train if you are based in Florence or Siena. The high-speed trains from Venice to Florence to Rome to Naples are much faster than driving and more comfortable than sitting in a car.
I might like a night or 2 in the Umbria region too, if possible. Train from Florence to Assisi for 1 night, train to Orvieto for 1-2 nights, train to Rome. Assisi is beautiful but only regional trains go there, so it takes a long time. There are fast trains from Florence to Orvieto and from there to Rome. You may find that you can rent a car in Florence and return it in Orvieto. That may be better if you want to see both towns. I used the train.
If you can fly home from Naples, then do go there from Rome for a couple of nights to see the Archaeology Museum and Pompeii. Otherwise, a long day trip on your own or with a tour is possible from Rome. A substitute is to visit Ostia Antica while you are in Rome.
Don't try to cram in too much. If you go to Naples, skip Umbria and base in Florence for other Tuscan towns. If you want to spend time at an agriturism in Tuscany with a car, skip Umbria. Count nights, 2 nights = 1 full day. Moving uses up about 1/2 day each time. Florence is very walkable, most of the main sights are no more than 15 minutes walk from the train station and your hotel will surely be the same. But getting around Venice is very slow and Rome is a big city, so between distances and traffic, it takes a lot of time to get from place to place.
Plan what you want to see and do in each place. If you want to 'wallow' in Renaissance art, allow enough time in Florence. If you just want to see the highlights (one day is enough), you may prefer to stay in Siena and day trip to Florence. That will help you decide how long to stay in "the big 3" and thus how long you have for Tuscany, Umbria and/or Naples. Some sights need to be pre-booked, the tour I mentioned in Venice, museums in Florence and Rome. September is still high season, I recommend booking all your hotels in advance. And you can save on train fares by buying tickets early.