Since you're planning on going as far as Polson, MT you should drive a little further and add Glacier NP to your trip. Drive north to Kalispell/Whitefish area and you'll be in fine shape to tour the park, more beauty than Yellowstone and not as crowded. Camp in the Whitefish/Columbia Falls locale and ride the tour bus if you don't want to drive Going to the Sun Highway. Yellowstone is a great park but in the summer it's just too crowded to enjoy the sights anymore compared to my first summer there over sixty years ago. Yellowstone is better in late September when the crowds thin out and the bison and elk are more accommodating.
