Okay, if you are going to go to Sequoia, then note that it is about 2 hours from Yosemite to the entrance of Kings Canyon, about 45 minutes to get to Giant Forest, and 5.5 hours to get from Giant Forest to Los Angeles. (These are usually the hours it takes us).
If you are going to bypass Hume Lake, and go straight to Giant Forest, then you will need to go to the Visitors Center there to get the tickets to go to Crystal Cave. I recommend visiting General Sherman, and taking the short hike/walk around Crescent Meadow. It is really beautiful there, and has a nice picnic area, flush toilets, etc. You can hike to a fallen sequoia tree called Tharpe's Log, that a mountain man made his home for 20 years each summer. The tunnel log is also there, and you can drive under it & take pics.
I took this last year of my family, on our way from Yosemite to Los Angeles, with a stop in Sequoia.
Leaving the Giant Forest, you'll pass four giant trees crossing the street (love to take a pic here. They're the last huge sequoias you'll see. You'll see the turn-off to Crystal Cave. You drive down a paved road to a parking lot, and then hike a quarter mile down to the mouth of the cave, where you'll go on a guided tour. Climb back up (steep) and then continue your way.
Be sure to stop at Hospital Rock on your way down the mountain. It'll take probably 2 minutes to get to the rock to see the native american petroglyphs there.
(I've made this trek several times in the past 10 years.
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