That is an epic trip -- but it is not at all impossible. Speaking as a Southern Californian, I would recommend not going to Southern Calif at all in the summer -- crowded and hot. The beaches are nice (especially in northern San Diego County), but otherwise it's an urban zoo.
If you want to stay as cool as possible, here are some ideas -- hit the north rim of the Grand Canyon. High elevation and trees. Yes, the south rim has somewhat better views -- but it is hot and crowded.
From there, head over to the Eastern Sierra -- perhaps the Bishop Creek area. The campgrounds are very high up and cool, and the scenery is pretty darn good -- this is Lake Sabrina:
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If you must visit Yosemite, the high country over Tioga Pass (Highway 120) is great. I try to avoid Yosemite Valley in the summer -- hot and crowded. But the Sequoias, an easy day's drive south of Yosemite, will have plenty of cool camping, and those trees are amazing and very peaceful:
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(To get a sense of scale, the yellow dot at the bottom of the picture is my wife.)
From there, you can cut over to the coast -- it would be a long day's drive from Sequoia to the coastal redwoods -- I recommend the Prairie Creek area -- it is cooler than some of the other groves. In the summer, the temperature rises a lot with every mile away from the coast.