July 23rd to August 3rd is a total of 12 days for this trip. IMO not enough time. Do you really have to get back on Wednesday vs. the second Sunday so you will have a full 2 weeks? A few additional days would greatly enhance the experience and reduce the "have to get there" pressures.
The best choice of the two RV parks you listed for Grand Teton is Colter Bay RV. The Virginian is in the town of Jackson with no views of the mountains. It appears that you want hookups and the only FHU campground inside Yellowstone is Fishing Bridge. Likely too late to reserve a site for this year, but you might get a cancellation. There are a number of private RV parks in West Yellowstone, with Grizzly RV the most recommended. Hopefully you are towing a car or plan to rent one when you get there as parking an RV at pullouts in Grand Teton and Yellowstone will be very difficult.
For a different route on the way home, consider leaving Yellowstone via the North entrance and pick up I90 at Livingston, MT. You can then use I94 across ND to Minneapolis. Along the way you will pass Pompeys Pillar, where Capt. William Clark of the Lewis & Clark expedition carved his name into the rock. This is the only remaining physical evidence of their trip. Easy off - easy on from I94. Just south of Bismark, ND is Fort Abraham Lincoln. This is the last post of General George Armstrong Custer before the battle of the Little Bighorn. There is a campground there with electric and water.
