4 Days in Yellowstone

We've been there twice. Personally I would just camp in one place the entire time. Use the time you would spend moving sites around to see stuff instead. You will see wildlife everywhere. On the roads, next to the roads, off the trails, etc. Otherwise I like your plan. Good mix of light hiking and off the road sites for a family.

If you plan on doing any hiking off the main roads, and I mean the back country trails not the "tourist" stops, even on short hikes, I strongly recommend good hiking shoes for everyone. Sneakers and sandles will just hurt your feet. Been there, done that.