lyoung3kids,
The Dordogne/Vezere/Lot region is wonderful. You will love it.
Comments re first day...Is Day 1 the day you are driving from Amboise? If so, I don't think you will have time to visit Padirac Cave and Rocamadour. I say this because that part of the region is further east than, say Sarlat, and will take you longer to drive there. Have you factored in, besides time on the road, gas and rest stops? The website Viamichelin is a good one for planning your drives, but does not allow for any stops. And once in the Dordogne Valley, you will not be on the autoroutes, and driving will be slower. If you miss seeing Rocamador, I wouldn't feel too bad. As often mentioned on this forum , the town has become mostly tourist shops, and is not as charming as it used to be. And in what town is Le Presidial restaurant? If you want to see a castle, I recommend Castelaud-la-Chapelle or Beynac.
With your very full plans for Day 2, I would try to go to Font de Gaume as early as you can get tickets for. The English language tours are usually only once a day, sometimes twice, but are offered late morning or early afternoon. (This may have changed though.) You will need 2 hours there (an uphill hike to the cave). And how much time does Rick suggest for the scenic loop drive? When and where will you have lunch?
We kayaked from Vitrac and it was wonderful! But allow 4 hours for this....Getting there (not difficult about 20-30 minutes from Sarlat), checking in and paying, getting your assigned kayak(s), going downriver (about 3 hours for a pleasant ride), putting in at the end, and getting the bus ride back to where your car is. So this will be a full day including your three activities. If you stay in or near Sarlat you will be between Font de Gaume and Vitrac, so convenient to both places, and in place for the market on Day 3.
Day 3 sounds okay (markets are on Wednesday and Saturday in Sarlat).
Have a great trip!