Another vote for Glacier RV CG, located about 2 miles W of the park's west entrance. Although when I was there, I had to go to the office for wi-fi, none at the campsites... not sure if that's important to you. But the sites were nice. In the park, there is a nice trail along the Lake MacDonald shoreline and a paved bike/walk path that runs back to the entrance gate. Get some ice cream cones and enjoy the lake view by the docks. The hike to Avalanche Lake was pleasant (moderate uphill going out and downhill going back) and the view at that lake was super.
Don't let the naysayers beat you down. You know what pace you and your family are accustomed to. You can fit it all in if you want to. I've done trips like that, covered a lot of ground and saw a lot of sights, and found the places I wanted to go back to and spend more time at some other year. It works.
Custer SP area is really nice, and the drive through the park (through the tunnels!) is very scenic with plenty of wildlife. I camped at a NF CG about 15 miles north of Custer, and that whole area is beautiful. Deadwood is a fantastic western-style, tourist-trap town to see, too, but I bet everything there is expensive; I only drove through town.
Be aware that driving through Yellowstone is a slow, lengthy process.
If you happen to exit Yellowstone via the west entrance, consider stopping on your way north for a meal at the Happy Hour Bar on the shore of Hebgen Lake (google it, you'll find the address). They serve the biggest, juiciest, best-tasting mushroom swiss burger I've ever eaten (and I could not finish the thing, it was that big).
