I would also advise you not to visit the national parks from one base camp. From your profile it looks like you might have a 29' RV. If so, why not stay inside each national park? It really doesn't take much to move from one to another and you will limit the miles you'd have to drive each day. Also, driving from park to park one time and finding out how long it takes and what little time you'll have to enjoy in the parks, I'll bet you don't drive to the parks more than once. That's not the way to explore a national park.
I-70 to 89 is an easy drive but don't be so concerned about mountain driving. You'll be in the west and you're going to have to do some if you want to see the beautiful sites. Your RV is small and you won't have any issues. Secondary roads are just fine. We used them with our 40' motorhome with no issues. You don't see anything via the interstates.