help with itineray

It really is up to you to choose what you most want to see, but traveling among Rome-Florence-Venice by fast train is the most efficient and makes good use of limited time. If you are okay with saving Venice for a future trip, and prioritize rural Tuscany with a car, then I think Florence-rural Tuscany-Rome would be a good plan. CT is very time consuming to get to, but you could add it if you don't mind shortchanging one of your other destinations. One night for CT is not great for someone wanting to do hiking, but you could certainly see all of the villages by train in a day.

If you head right to Florence on arrival and out all Rome nights at end you avoid that split stay/1 night in Rome at end which is sort of a waste

11 nights
Arrive
Train to Florence
Florence 3 nights
CT 2 nights
Pick up car- which you will need for Tuscany
Tuscany- where exactly? 2 or 3 nights
To Rome- drop car
Rome 3 or 4 nights

FWIW I would pick Venice over CT
To Florence 4 nights with 1 day trip
Venice 3
Rome 4

No car needed
Start planning trip #2

3 nights in Rome a two in Florence is just not enough time. Suggest skipping CT.

I would skip CT and add time in either Rome or Florence or do a 1 night stay in Orvieto which is closer to Rome. I agree that you should avoid splitting your time in Rome and go there at the end of your trip. Take a train to either Orvieto for 1 night or to Florence when you arrive in Rome.

I would do:

Day 1-4 Florence (3 nights)
Day 4-7 Tuscany Agriturismo OR Venice (3 nights)
Day 7-10 Rome (3 nights)

You could also stay longer in Florence and do day trips to explore more of Tuscany rather than switching locations entirely.