Provence and the Dordogne, too much?

Sounds like you have 3 weeks? Its not too much at all. But I question using Nice as a base for Provence. Nice is about 2 hours away from Provence. The Dordogne is about 6 hours from Provence, so you could get there in half a day. Perhaps consider breaking up your stay in Provence into two bases, one in Provence proper and then the second on the Cote d' Azur, which is technically where Nice is...

Two weeks in Nice is too long, in my opinion.

Nice is the farthest part in Provence.
Regarding going from the Dordogne to Nice :
No, this not to much ground as there is no standard amount of time; everyone finds their own pleasure traveling differently
You can always Google the map of France and see travel times and definitely should get a guide book; that will help you save time getting organized.
I visited the Dordogne over xmas break covering Sarlat, Montignac, Lascaux, and La Roque Gageac.
Most who have been to the Dordogne area see a car a to get around is essential.

It's not too much ground to cover, but you should plan carefully about how many nights in what place. Nice may technically be part of Provence (I'm not sure), but it's pretty far from what most us would think of as Provence (Avignon, Arles, Aix-en-Provence, St. Remy, etc.) So really you would be visiting three regions in practical terms. I have been researching this myself, and flying into Toulouse might be a good choice. You don't want a car in Nice, it's a big city. You would probably want to stop a night in transit in Carcassone on the way from Dordogne to Provence. (My wife and I passed through Dordogne-Carcassonne-Arles-Nice in 2003 as part of a France trip. It was only seven nights as part of a longer trip, much too short.)