Trip from Lucca to Rome...where to stop for a few days in between?

Orvieto! However, if you're looking for a 1- or 2-hour stop, there are probably many better alternatives. Orvieto isn't just a beautiful hill town; it has many actual sights and it justifies a stop of even more than one full day. Rick has a good write-up about Orvieto in his book on Italy. You will not be the only tourists there.

If you should decide to wander over to the west of the direct path, Tuscania is a very attractive, quite non-touristy town. It tends to be dead during the siesta period, I think.

Closer to the highway is the city of Viterbo, with its historic district still walled. Also not very touristy.

One of my favorites is almost halfway between Lucca & Rome. Montepulciano is smaller but is wonderful to explore. I stayed there three nights during a summer month and loved it. Use the parking lot near the bus station (looks like a 7-11) and take the small orange shuttle up, up to the top. I think it was 1.5 Euro. There’s several smaller towns nearby to drive around & see.

Also, on your way to Montepulciano, stop at Siena if you haven’t been there previously. The Campo piazza, the cathedral are well worth seeing. And you can climb the clock tower at the Campo for some great views. For the age of your kids, I might stay in Siena, and just stop at Montepulciano on your way to Rome.

You might decide it’s less stressful to just return your rental car in Chiusi near Montepulciano and take the train into Rome.

Arezzo is not far from the autostrada and is worth a whole day.
Lucignano is tiny, ideal for a short easy stop to stretch your legs and have coffee. A hidden gem, Tuscany at its best.
This was a day out in Arezzo and Lucignano:
https://slowtravelitalyspain.blogspot.com/2020/11/tuscany-september-2020-arezzo.html

Cortona and Arezzo, 20 minutes apart. Orvieto, as someone mentioned. Also, there is Lake Trasimeno. I don't know what it would be like in December, though.