Let me add a few suggestions to the route already in the mix. First, you can get a lot of information about the National Parks and National Monuments by plugging them into the internet or from the NPS website.
Even if you can't get a campsite inside of the major parks, all of them have numerous commercial RV parks near them so that should not be a major problem. You don't say just what sort of things interest you, but most of the itinerary suggested is pretty much what I might do, but I would add Antelope Is. State Park
just to the north of Salt Lake City.
After you leave Glacier NP, you may want to travel west to see Mt. Rainier Natl. Park.
From there you should go south and see Mount St. Helens NP,
the big volcano that blew up about 30 years ago. Once you leave there you should go over along the Oregon Coast and follow that south, visiting a few Oregon Lighthouses
as this is some of the most spectacular coast in the world. It would then be a fairly short run down to Redwood Natl. Park.
Leaving the redwoods you should probably plan to make a quick stop to see San Fransisco if the city is of any interest and then make a trip to see Yosemite Natl. Park
. Between this and your return to Vegas would make it handy to make a stop at Joshua Tree Natl. Park
With what amounts to two months to travel in, you will have a very full itinerary. The trip which I have just outlined will require the driving of more than 4,000 miles or 6575 kilometers. If you are to cover all or most of the suggested itineraries then you will have a very long days or very short stops. To see the Grand Canyon requires several days. The same is true for Yellowstone and at least two for Glacier. You may need to plan this to have somewhat fewer places to visit and less time driving, or you can make some long driving days between stops.
Traveling with the RV you can expect to average around 50 mph or 80 kph. that means that you will have about 13 days of just driving, if you travel for 6 hours each travel day.
You can do this but you need to realize just how much travel we are suggesting.