Probably, you only have 8 nights in Italy plus two days getting to and from Italy. So, it would be good to think of exactly what it is you want to get out of this trip. Two destinations only, possibly three depending on the ages of your family members. Otherwise you are spending most of your time en route instead of being anywhere.
You could fly into Venice, stay in Venice for a few nights, then drive or take the train to Florence or Siena for a few nights. If driving, you could stay at an agriturismo in Tuscany. If taking the train, you could stay in or visit any town in Tuscany that you can get to by train. Fly home from Florence (so easy!)
You could fly into Rome, stay in Rome for a few nights, take the train to Naples and then onwards to see Pompeii, staying for a few nights in whatever the town is that Rick Steves always recommends (we have only stayed in Naples and in a hotel next to Pompeii). Fly home from Naples or Rome.
I keep saying "a few nights" because it depends on your own interests --- your 8 nights could be divided up any way you want, even 2 nights + 6 nights.
You do not need or want a car unless you want to drive around seeing the countryside in Tuscany or to drive on your own schedule from one Tuscan town to another on day trips.
I'd like to say here that I am sure there are parts of Tuscany that are magically lovely like you see in photos, but so far the parts of Tuscany we have driven in, taken the bus in, or ridden a train through, look like normal, real life with gas stations, some ugly buildings, big stores, parking lots, signs, traffic, trucks, etc. We enjoy this sort of thing (actually much more than we like pretty scenery) --- it's interesting to see what you can buy at the truck stops, for instance, or to see what a regular, non-lovely farm looks like, or to figure out how to pump gas. Many famous medieval hill towns are, of course, surrounded by their newer and less attractive regular parts of town (this is where you will be parking the car). So, if your dream trip to Tuscany is to drive around in beautiful scenery, get advice from this forum on exactly where to go.
As for driving vs trains, driving in Italy is just fine and Italians are way, way better drivers than the drivers in American cities and on American highways. Just learn what to expect, what the signs mean, have a "navigator" who can use Google (or other) maps on a phone while you are driving, and know where to park outside of the historical center of every city and town. The trains are great, the train stations can be a bit bewildering and crowded. Again, learn what to do before you go, especially if any of your family are young children --- they may be less tolerant of waiting around, getting lost, standing in line, finding the bathroom, etc.. The RS books and this forum will help you know what to expect and how to handle things like validating your tickets.
With a car or a train (or a bus), you'll be doing much more walking than you may be used to and probably taking taxis, too. And, at many points, carrying all your luggage.
I hope none of this sounds discouraging! We go to Italy for several weeks every year and always love it. We've driven long distances in Italy (like, Venice to Sicily), driven in supposedly scary places and in tiny towns and have gotten only one parking ticket, rented a 9-passenger van so that we could take family with us, and used all kinds of public transportation both between and in cities. You can do it!