If you want to head east on I-70 from Moab one way to Rocky is to take Hwy 13 at Rifle, CO (Rifle Gap or Rifle Falls are nice state parks if you need to stay a night). Take 13 north to Craig, CO and east on Hwy 40 to Granby and on to Grand Lake (nice camping) and then take Trail Ridge Rd. from the west into Rocky Mtn. Nat'l Park. Be warned that it's a steep drive but many RVers do it. We have. It's all a very scenic drive and you wouldn't have the Denver mess to plow through.
Someone mentioned construction and delays in Arches Nat'l Park and yes, the campground will be closed all summer and there will be road delays. However, there are plenty of places to stay in Moab (Dead Horse Point State Park at Canyonlands is very nice) along with many RV parks. Plan to get to Arches by 7 am or even earlier for your touring. It would be a pleasant time of day. Also, if you can make reservations, the ranger-led 'Fiery Furnace' hike is awesome but very popular so get reservations early.
Have a great trip!
Here is Arches' web site where you can read about the 2017 construction project and other helpful information. Each national park has a great web site so check out Rocky Mtn., also.
https://www.nps.gov/arch/index.htm