I think the suggestion of two class C rentals is a good one. I would suggest you pick one area to concentrate on. Trying to do too much will just equal a lot of driving. This wont go over well with small children. Myself personally, I would choose the Grand Canyon area, and southern Utah. World class scenery. You could start in Las Vegas, or Phoenix. I have only done these in the winter months, but someone else might be able to suggest the best off season time to see these places. I would think after school starts in September, it would be less crowded, but the weather would still be nice. My second choice would be northern California and Yellowstone area.
