I'd cut out California and save the whole west coast for another time.
A great family trip would be to head for the Black Hills of SD for a week at Custer State Park as your base (or a commercial CG) and then go down to Cody, Yellowstone and Grand Tetons NP.
Then swing south. You could easily spend a month enjoying the Four Corners area ... Utah's fabulous parks alone are a trip of a lifetime, but you also have Mesa Verde, Monument Valley and much more.
(Actually, for June and July, I'd go south first and then up to Yellowstone in July.)
