We can't speak for the Grand Canyon but you will be fine in Yellowstone. We had our dog with us and were limited to the parking and viewing areas. In a number of stops they have wheelchair accessable paths if you need them. You can see an awesome amount from the car and stops along the way. We hit just about every turnoff in the park, and the difference, from the multiple canyons, that large valleys, the waterfalls, etc; it was a fantastic trip. We just spent 8 days there then 5 in Grand Teton and I think you will have a great time.
2013 Chevy Express Van 1500 with 2500 rear end
2017 Jayco 23MRB: 26' total and Glacier Package
Married 43 years. Aki the "mutt," 12 years old "Excited to learn new things everyday and humbled by those who offer to help."