You have plenty of time to enjoy this trip, it's positively relaxed when compared to what most try to cram into a trip. You could actually add a few bits to your trip, Monument valley, Bryce canyon and Zion would be well within the scope of your trip but might feel too rushed for you. From Sedona you could easily drive to Monument valley and spend one night and enter the Grand canyon via the east entry kiosk along Desert view drive. I would actually use this entry point whether you visit MV or not and make your way to the main canyon area in the same direction as the Colorado river does. Desert view drive has a few viewpoints and it will save you going back and forth along it, and somehow I prefer it to arriving in the middle of the park, through the south entrance. I just like the build up to the 'main show', starting with the expansive views from the Watchtower of the Colorado river and surrounding scenery before the 'Grand Finale' ! [Near to the east entrance is the 'Cameron Trading Post' which is worth a visit and if needed, has a basic RV park across the road from the restuarant and shops.

You will certainly need to book RV sites in both Grand canyon and Yosemite as soon as the booking window opens [check the dates at nps.gov] as they can sell out in no time at all. Make a note in your diary ! You might want to book others as well, [?] there are limted sites around SF for example. For GC, the Trailer park has hook ups and Mather campground doesn't, both are near the village, the rim and the shuttle bus service to Hermits rest etc. I would recommend one of the three 'Pines' campgrounds in Yosemite Valley, again a free shuttle bus service is available nearby and means you can leave the RV where it is and enjoy the park for much of your stay.

You could consider handing the RV in as you reach LA and find lodgings, it'll be a bit of a beast to get around the City ! As you are considering another visit and leaving LA for that time, I would certainly look at Bryce and Zion NP's as an option and end in SF, I know which I would prefer, but that comes down to personal choice.