Where would you stay in between Rome and Florence?

Before you get too far, consider that you will need to rent a van to hold six people and luggage.
On arrival day with jet lag, I would drive no longer than an hour--I am afraid that does not even get you to the border with Tuscany. Could you work it so you take a train to Florence on arrival day, start there, then do your rural stay in the middle, then finish in Rome?

I’d drive no further than Orvieto

Better yet-on arrival take train to Florence then pick up car as you leave Florence ending in Rome

Before you get too far, consider that you will need to rent a van to hold six people and luggage.
On arrival day with jet lag, I would drive no longer than an hour--I am afraid that does not even get you to the border with Tuscany. Could you work it so you take a train to Florence on arrival day, start there, then do your rural stay in the middle, then finish in Rome?

Yes, I do know that I would need a small van. It's tough, because the only way to see some of the small towns of Tuscany that we want to see is via car rental.

If we took a train from the Airport to Florence, and then drove to Tuscany during the middle of our stay, that only really helps that I wouldn't have to drive right off the plane. It doesn't shorten any of our travel time, unfortunately.

The plane ticket prices dropped substantially so I booked them, flying in and out of Rome. I knew we would have to deal with some inconvenience, as opposed to flying into Florence and out of Rome.

I see what you all are saying. I will talk with my Agriturismo and see if I can move our stay up 2 days..

Basically, train to Florence from the Airport. Looks like that's about 2:20 with a stop at Rome Termini. Then, I won't have to be in a car on lack of sleep. Spend my 5 days in Florence, and then when we want to leave and head toward Rome, we can be fresh, drive to Siena, Pienza, etc, and Finish by dropping the car off before getting to Rome (likely either FCO or Orvieto, then train to Rome).

Yeah no getting around that, just making sure you had looked into it. If you can drive/park a regular car, you can drive/park a van--you just might be a bit more particular about said parking space!
I think you first have to think about how long you can reasonably (safely) drive on compromised sleep (It gets some people riled up, but it is a serious safety concern). With no kids, we have set our personal limit at very much less than two hours. A delay (flight, baggage, whatever) can really eat into your day, so you also might be setting off later than you plan (been there, done that). Not having to drive immediately reduces that stress, hence the suggestion to use train on arrival and put the drive in between two city stays. There is no right answer, just lots of variables to ponder.
Another lovely town less than two hour drive from FCO is Pitigliano. I think kids would love to see a vie cava and there are several around Pitigliano. https://www.wanderingitaly.com/maps/vie-cave-pitigliano.html!

Note that your only rental option for a drop off in Orvieto will be Hertz
( AutoEurope does not work with that agency)

Options for drop off in Chiusi will be Avis/Budget

What day in March? Italy (Europe) switches to Daylight savings on the last Sunday of March, which in 2025 is March 30. Before then Sunset will be before 6:30pm. If you land at 2pm don't plan to be driving out of the airport car rental lot before 4pm. You'll need 3 hours to reach the Val D'Orcia from the Rome airport, so it will be dark and not so safe considering you will be jet lagged, unfamiliar with the roads, and driving on curvy narrow roads after Chiusi. How about stopping on Lake Bracciano, at Anguillara Sabazia or Bracciano, which are pretty (even Tom Cruise had his wedding there) and less than one hour from the airport, then proceed the next morning to the Val D'Orcia via the Via Cassia (SS2) the old highway from Rome to the Val D'Orcia, which is a pretty ride?

Bracciano and the lake it’s on is one of those undiscovered gems most travelers never get to see as it’s just not on their radar screen.