Wow, those distances are pretty vast. I guess if it were me, I would do it myself -- book the flights, rent the cars, etc. With this and other online traveler sites, all the info you need is available. Just know that US National Parks in the summer are VERY crowded. The hotels are booked. The roads are a parking lot. 'Not a lot of fun. If there is any possibility to travel in September instead, I would do that. about 6 years ago
That is alot of ground to cover but not impossible. Agree you should look at doing it by car and exploring them with some possible National Parks pass that may be available from the National Parks website:
I am not aware of a t that covers all of them and it's nicer to go at your own pace with a car rental. Besides, there's lots of other parks and things to see in between these three parks you listed.
Check out nationalparksblog.com for the latest on what's going on with some parks, national and state ( some are closing because of budget cuts).
And book what you can by way of lodgings or campsites in or near the parks. They do get crowded in the summer, and with the long recession, many Americans more than ever are staying domestic for holidays and going the budget route, both which further point to more crowds in many parks across the country.
Enjoy! Yellowstone and Redwoods are on my top list. about 6 years ago