Hi there, Sidewinder -
The entire trip is about 8.5 days Arriving at 1130 for the .5 and
leaving on the 9th day.
So realistically, this only gives you 7.5 days for a proposed (including that day trip; Lucca+ Pisa is a DAY trip, IMHO, not 1/2 day) itinerary of 5 destinations. So, ouch? Lots and lots of travel and not much time in those destinations themselves. Cutting the CT and giving you those 3 desired FULL days in Rome, I'm seeing a feasible schedule something like this:
1 - arrive Venice (partial day)
2 - Venice
3 Venice> Florence (partial day)
4 Florence
5. Florence>Rome (partial day)
6 Rome
7 Rome
8 Rome
9 Fly home
(Editing to add: you might be counting differently, with a .5 day before my day 1? If so I'd add the extra day to Florence for a day trip)
If my count was correct, there is no time for random side trips here - not even for Pisa/Lucca if you want to do Florence any justice - and none of these destinations are vehicle friendly. That includes the CT, should you drop Florence/Pisa/Lucca altogether and move those 2 nights there.
The plus of using the trains is efficiency when time is limited: you can get on one in the middle of one city and get off smack in the middle of the next. There are no worries about parking ( inconvenient, expensive, and a lot of city accommodations don't provide it), avoiding bus lanes and no-drive zones/ZTLs (read up on those if you haven't) or safety of leaving your luggage in an unattended car if making random stops, even if you did have time. The high-speed trains will get you from city-to-city much faster than by road.
Anyway, for a 7.5-day, 3-city trip - or even 2 cities plus the CT - I'd go with the trains. A vehicle can be fine for a trip devoting adequate days to exploring rural Tuscany, Umbria, Dolomites, etc. but I really think it would be more hassle than help for your particular trip. Realistically, you have less time than you think you do so I'd encourage some prioritizing and rethinking of your transport plan?