Advice for Yellowstone Trip

[helptheold]

I'm in the final stages of planning our Yellowstone trip this July and am a little stumped on how many nights we should stay in Grand Teton, Dinosaur National Park & Salt Lake City.

We're flying into Bozeman on a Thursday, staying in Yellowstone for 5 nights then planning to drive down through Grand Teton then veer southeast to Vernal to Dinosaur National Park, then head west to Salt Lake City to leave the next Saturday.

So my plan is to spend 1 night near Grand Teton in Jackson, 1 or 2 nights in Vernal and 1 or 2 nights in SLC. We have to be in SLC on Friday night as our flight leaves 11 AM on Saturday.

Which would be better to spend 2 nights in, Vernal or SLC? Can you do the basics in Dinosaur in a day? Keep in mind I've got two teenagers who are not into the outdoors so they may be hitting their limits by then!