CINQUE TERRA - after Bologna and en route to Montepulciano

LaSpezia has a number of rental car companies and reservations can be made online. Many of the smaller cities in Italy are without rental car agencies. I'd pick up the rental car there and drop it in your city of departure.

You can find a bunch of hotels on Montepulciano online at Tripadvisor or Booking.com. It's large enough to have decent places to stay.

Many would look into agriturismos--farm stays. There are a number of nice places outside of the city center, and they'd work since you have a rental car. They're available at VBRO, Tripadvisor, Booking.com an Agriturismo.com.

Between LaSpezia and Montepulciano, you can visit the great hilltown of Volterra.

Check the hours at the La Spezia rental agencies. I think you'll find it difficult to visit CT for the day and get back to the rental agency in time to pick up your car. Even if you can then the day is gone- not much time to drive around "Western & coastal Tuscany and Volterra as we drive"

Spend 2 nights in La Spezia and pick up your car first thing in the am to get the most out of that day and the rental.

Since you’ve never driven in Italy, scroll down to yellow banner and download their E-book. Italy has some driving rules that could cost$$$ if you break them.

https://italybeyondtheobvious.com/

You definitely do not need a car in the Cinque Terre. Parking is almost nonexistent. Rent your car as you leave, either in LaSpezia or take a short train ride to Pisa. Which would be closer to Volterra.

How many nights do you have for this trip not counting travel days?

2 nights from the time we exit Bologna and get to multipulciano

multipulciano

MONTEPULCIANO

Be sure to check train times, as that can affect how long it will take you to get to La Spezia. Why are you are not staying in CT? You should definitely do both nights in the same place regardless.
If it were my trip, I would just take a train to Florence, get a car and enjoy five nights in Tuscany.

Take train to the village of Cinque Terre of your choice and stay there.

I see no reason to stay in a hotel in La Spezia, which is a pretty ugly port town in my opinion.

Then the morning that you leave for Montepulciano, take the train back to La Spezia and from the station take a taxi to the rental agency (all rental agencies are near the cruise port).

To go to Volterra from La Spezia you'd go to Pisa then take the Strada Grande Comunicazione (SGC) FI-PI-LI (Florence Pisa Livorno) toward Florence and exit at Ponsacco, then from there take the State Route (SS439) to Volterra.

The freeway from La Spezia to Pisa runs along the coast but a couple of Kilometers (about 1 mile) from the water therefore you won't see the sea at all from the freeway, unless you exit the freeway at the Versilia exit and head west to the beach at Forte dei Marmi. Forte dei Marmi is an upscale beach town. Not a Caribbean beach, but the town is nice with lots of rich people villas (Andrea Bocelli lives there) and plenty of high end shopping (Prada, Gucci, etc.).

Just be aware that, even without pit stops, from La Spezia to Volterra is well over 2 hr drive.
Then from Volterra to Montepulciano it is at least another couple of hours on winding roads.
So curb your expectations, as there are only so many hours in a day.