Dear OP
I agree with the others that it’s better to stay in one place and take side trips, as you will on your cruise, unless your family really loves road trips. My wife and I learned that we wasted far too much time and energy traveling, checking in, and unpacking/repacking when we had a more ambitious itinerary.
Our kids enjoyed playing far more than sightseeing in cities, which got old pretty fast. We found that beach access or a pool were essential.
Driving: I thought it was fine. Italians are generally good drivers; excessive speed rarely an issue, because of the omnipresent toll cameras on the autostrada
We rented from Avis because the had an extensive network of off-airport locations and allowed us to pick up in Florence and drop off in Rome. We used our Costco codes even though you can’t book Italy directly through them anymore.
We checked rates daily, re-booking when they dropped until we locked in at a rate we liked.
Have a debit card for gas. Many gas stations are automated and don’t accept cash or credit
Activate the toll transponder. It’s easy to go through a malfunctioning booth that won’t take your debit card, and many toll plazas are automated as well. Even if you pay the toll online afterward, as we did, trying to avoid a fee from Avis as well as an Italian penalty, we were still charged by Avis (6 months later) because the highway authority had already transmitted the violation
Italian cities often may have restricted central zones for taxies and locals, but but guests at certain hotels with the zone may be permitted entry. If you stay at one of those, make sure that the hotel actually sent your info to the police. We received another Avis fine and one from Italy as well because of a breakdown somewhere in that process.
Have a great time, whatever you do.