I can tell you that your rig cannot fit into the southern Joshua Tree campground (Cottonwood). I know this because I have tried it, and I have no towed vehicle! However, Indio and Palm Springs are very close and have lots of full and partial hookup campsites. There is one campground (Black Rock) in the northwest part of the park, you possibly could fit into, but the sites are dirt and I can't remember if they have electricity. ON the north edge of the park, there are also several commercial campgrounds very close to the northern entrance, so very easy to stay at and drive in for the day.
As far as Yosemite, there are several huge campgrounds there, but none of them have electric hookups, though it is really worth staynig there for at least a few days. You will just have to dump your tanks and refill with water. I have stayed there in my 32 foot C, but just make sure you pick your site carefully, and it is large enough length-wise and width-wise.
You can stay outside of Yosemite, but it is a very long drive into the park each day. And during summer, there could be a lot of traffic in and out.
It is good you are starting early to make reservations because national parks fill up quickly. Read a lot of campground reviews and use Google maps to view the places, if you can. This site also shows photos of many campground sites:
CampsitePhotos.com - Campsite Photos and Camping Information
Also, a warning--state parks in California are very expensive and very basic, so what I have been doing is looking at county campgrounds, which tend to be much nicer and with at least electricity, for a lot less money.