We have done two trips out West. Each time, the trip was a limited opportunity to go.
We elected to jump around as much as we could to see as many different places as we could. It worked for us.
The first trip (1998) was 26 days with car, tent, bicycles and no kids. The second was 30 days with MH, Toad, bicycles and two kids.
I think a second type of transportation will help tremendously, specially if you are trying to squeeze in as much as you can in a short time.
Although I would not like dealing with a trailer behind a MH, you must be use to it. With many stops in a short period of time, hooking and unhooking might get old. Many do it with TT or 5ers. However, I didn't see many campsites long enough for both rigs. If you research and find pull-throughs along your route, that would save some time and hassle. Otherwise, it's drop the trailer in the storage area and go to your site to set up. When exiting CG, do the reverse to get back on the road.
Busses, shuttles and rentals take time. Even if a shuttle stops right at the CG, you will often wait. Otherwise, you will have some trouble finding parking for an RV at a lot of stops. Parking for the TOAD was difficult at a few popular National Parks, but for the most part, we were able to drive right to a trail head/overlook/visiter's center and park quite quickly. It helps if you are early risers.
On the 1998 trip, we went to Yellowstone, via Badlands, Mt. Rushmore, Wall Drug, Crazy Horse and Devils Tower. We had to drive much further than you (Morgantown, WV which is about 1.5 hours south of Pittsburgh). After Yellowstone, we skipped down to CA through Lake Tahoe, hit San Fran/Muir Woods, Yosemite, Sequoia and Vegas to see family. On the return trip, we stopped at the GC, Zion, Arches, Bryce and Rocky Mountain. Some of these stops were only one night with a visit to some overlooks. Hey, it beats never seeing it in our lifetimes right? Was it worth it? You bet! We didn't get back West until this past summer.
The 2015 trip went in the reverse. We went to Moab/Arches, Bryce, Monument Valley, GC and then to San Clemente for a wedding. After that, we went to Sequoia, Yosemite, San Fran/Muir Woods, Yellowstone, Mt Rushmore and home.
The drive from San Francisco to Yellowstone took two days from our trip. It will be a similar trek for you to Yosemite. I would have much rather maximized our time in the Southwest, but now that my kids have seen Yellowstone, I'm glad we did it.
A trip similar to what you propose is possible. I think 19 days to swing out to California might be pushing it. You might if you use I-70 as your return route and count on just stopping off for quick visits at some of the parks along that route. This is what we did in 1998. This plan makes the Grand Canyon a tough stop. We did the North Rim in 1998 after stopping at Zion. Zion and Arches were our favorites, so we planned longer stops there on the second trip. We went off-road around Moab. Visited Canyonlands, Dead Horse Point and Pink Coral Sand Dunes SP while based in Moab. This route set us up for Monument Valley/Four Corners and the GC en route to the wedding in San Clemente.
If you skip the California leg and miss Yosemite, you could drop down to the GC from Yellowstone and maximize your time around that area. Walk the Narrows in Zion. Drive the entire loop at Arches and take some time to walk some of the trails there. You can't go wrong with that.