Itinerary help Loire and Dordogne

There is a very recent thread on a similar topic:
Here
3 nights is really rushed to make that long drive through two thirds of the country.
If you are 100% set on driving, I would shorten the route as much as possible, skipping Dordogne altogether. You could do, for example, 2 nights in the Loire and 1 night in Pérouges near Lyon to check the "cute village" box.
Make sure that you are not planning to drive to Nice on a Saturday: traffic towards the Med is terrible on summer Saturdays.

If you are open to other options... How about 3 nights in the Loire and driving back to Orly for a flight to Nice ?

In July, during the weekends you will be in the usual summer traffic jams (800kms cumulative of traffic jams each weekend during July 2022).
Especially if you go to the French Riviera in Nice.

Moreover, going to Sarlat and staying there only one night is totally useless.
Sarlat and the Dordogne need to stay there at least 3 whole days to be appreciated.

From Sarlat to Nice it's at least 8 hours of non-stop driving.
This means that when you arrive in Sarlat you will spend at best a few hours there in the afternoon and a dinner, before leaving the next day as soon as possible.

In your place I would drop either Sarlat or Nice.

Not an expert, only a traveler who loves France. I agree with others suggesting dropping either the Loire Valley or Dordogne. My recommendation is to drop the Loire Valley and keep the Dordogne. In the time your family can tour one chateau you can see much more in the Dordogne. Sarlat is truly a wonder but will be overcome with tourists in the summer. My suggestion is to research https://www.les-plus-beaux-villages-de-france.org/fr/nos-villages/ Les Plus Beaux Villages and pick three charming villages in close proximity to self tour.

I don't have children, but I urge you to make sure that 3 nights in crowded Nice will be of interest to them. Some people who live in landlocked United States want a beach during their European vacation, but that seems to me like an expensive day at the beach. Is it realistic to believe that none of your children will ever visit France again in their lives, and have an opportunity to visit a region that they missed with their parents?

I know I can't talk people who love to sit in their cars (have you checked rental prices, drop-off fees, and how cramped you'll be without the mighty SUV you use at home?) out of long drives. I agree that five train tickets start to add up, but driving is not cheap these days. You are not going to see any sights from the highway.

Thanks everyone. I hear you about the long drive combined with summer traffic.
We could drive as far as Toulouse and take a hopper flight to Nice since we don’t need a car there. We planned to take the local train to towns between there and Monaco.
I’ve wondered if we really need 3 nights in Nice but also figure we will be tired by then so an extra day to relax would be nice. From Nice we head to Berlin for 6 nights in Germany.
As a complete alternative I’ve considered 2 nights in Loire and 1 night to see St Mont Michele then go back to Paris to take the train to Nice.

You definitely need those three nights in Nice.
Your alternative Loire + Mont Saint Michel is so much better IMO.
And you can fly from Rennes to Nice nonstop on easyJet. Or Nantes to Nice. Both are more convenient than driving back to Paris.