OK first stab at the plan.
Location Nights
Los Angeles 0
San Diego 2 (Wed, Thur)
Palm Springs 2
Las Vegas 2 (Hoover Dam, Grand Canyon Helicopter) (Sun,Mon)
Mt Carmel Junction 1 (Use as base for Zion, Bryce, Horseshoe, Antelope) . <-- Too many things and not enough time, so will consider more.
Death Valley 1 (two minds about this, going to be too hot, but the Mrs loves stars and apparently it's awesome for that.)
Mammoth Lakes 1 (I put this in as mentioned a fair bit in this thread, need to investigate)
Yosemite 3 (Just outside)
San Francisco 2
Morro Bay 1
Los Angeles 2 (Universal) (Friday)
Understand the times and distances here, Zion and Bryce as big places - whilst there's only 72 miles between them on the map, understand that in the daytime those roads are slow and those parks are big.
Also, honestly - to make something like Zion worth it's while, you need 2-3 days minimum, yes - you can simply drive the road through the park, but there are a lot of incredible hikes and other things that most people just drive past and have no idea about. Last time I went I hired a wet suit and some canyoneering shoes, and did the 'subway hike' which takes a full day, but it was absolutely incredible from start to finish, just - magical in every way, thats a very difficult hike - but there are many others to chose from, the slot canyon hikes are amazing.
https://www.citrusmilo.com/zionguide/lowersubway.cfm
But it depends what you want to do, if you just want to drive and not do any hiking - going to places like Zion or Bryce you're only going to see a small part of them, for what is a lot of driving.
Horseshoe bend is good very very busy now - lots of coach fodder, they've built a new car park, so in August it'll be attracting hoards of buses full of locusts - I have a low tolerance of this sort of thing, but you might be fine with it.
Antelope is a mixed bag, VERY busy - it's an incredible place, but the natives really reap that place for everything it's worth - imagine 50x people crammed into small spaces, the place itself is incredible but again, think about whether you enjoy being with that amount of tourists in small spaces. You can do some research and pay a bit more - you can get private tours from some of the other Navajo families who own other slot canyons next to Antelope (there are a number of different slot canyons in that area)