Welcome!

The easiest things to see from LV to LA would be the Mojave National Preserve and/or Joshua Tree NP if you are looking for nature. Another option would be Death Valley, but that may cut your time too tight.

The most common route from LA to SD would be I-5, which is pretty solid urban and suburban all the way - and quite congested. Disneyland and Knotts Berry Farm are on the way, as is Legoland in Carlsbad. Another option is head east and go down I-15 to the Escondido area and see the Safari Park. It's operated by the SD Zoo. You can buy a ticket package which would also include the zoo.