There is no good way through or around LA. I just did a google maps and it says 6 hours and 20 minutes from SD Zoo to Yosemite. No way in *****. I'm on my phone so I can't force a route real well but you could take I-15 East of LA to 395 to 58 which will get you to 99 at Bakersfield. You can force that route in a computer and see how long it says. You will still need to time I-15 right but near as much as I-5.
From there it's easy. Fresno to SD is 6 hours 99 to I-5 if you time it right. 9 hours if you don't. I just don't think I'd want to drive I-5 at anytime of day with an RV except maybe 0300 in the morning.
On Yosemite, Your three main options are Coursegold on 41, and then off 120 or 140 NW of the park. Coarsegold is probably an hour to Tunnel View. Another 20 minutes to Curry Village in the summer. Where is your reservation? There is a little town called Fish Camp just south of the Hwy 41 entrance but I don't think there is an RV Park there. We've camped off 120 before but you have to go over a pass so it was a solid hour from the campground to the valley. I don't remember the name, sorry, but there are lots of options. We've camped off 140 once as well and I think it was closer but it's been 6 years and just don't remember. With a pop-up and the bears, we usually rented one of the Curry Village options. As a relative local, we also visted off-season so it was easy to get a heated tent or room. Where is your reservation?