I'd either do a Yellowstone/Grand Teton/Black Hills trip in late June or a Grand Canyon/Zion/Bryce trip in mid September. To try to see both the Grand Canyon and Yellowstone isn't going to let you "experience" either one with the drive time from Chicago. These are big states and long distances to drive between those two parks. Driving an RV isn't like a long distance motorcycle trip. Slower, more stops etc.
To try to get from Chicago to Yosemite is over 2000 miles = four very hard days of driving. You'd use up a big chunk of your vacation staring at your windshield.
Unless this is the only chance to go before you get rid of the RV, break this up into several trips and enjoy the places you go. For instance, even on motorcycles, it takes several days to see Yellowstone. With two big loops, low speed limits and "buffalo jams" one doesn't make great time through the parks.