I think I'd forget about Redwood NP in California and concentrate on the wonderful SW national parks. Head to Grand Canyon first then do the southern Utah parks - Zion, Bryce, Arches, Capitol Reef then head to Grand Teton which is next to Yellowstone, then over to Mount Rushmore and home. You'd have a fantastic trip in 7 weeks.
You didn't say what you'd be traveling in but our 40' MH fits in all of the above parks - been there often and without reservations. However, we don't do in prime time. I'd recommend you try for reservations IN each park for the best overall experience. Some of the parks even have campgrounds that don't even accept reservations, such as Grand Teton and Yellowstone. Go to each national park web site and you'll find all the campground information. Have a great trip but get working on a plan - NOW.