Are you renting a small motor home like Cruise America? The Pacific Coast Highway is breathtaking and I would normally recommend driving from Malibu to Monterey but it is winding and cliffside for parts of it so I wouldn't do it with a trailer in tow. If you are in a Cruise America style motorhome it might be possible but borderline.
Really nice aquarium in Monterey that the kids would love. You could keep soing to SF and catch the Golden Gate Bridge and Fisherman's wharf for a quick half day and then head towards Yosemite. For Yosemite, I would look at private campgrounds on Hwy 120 or 140 and stay the day before you visit. You could go in and out each day - I've done it - but it's an hour drive. The other option is break camp and do Yosemite for a day and then stay south of the park on Hwy 41 on your way back down to LA. The hike to Yosemite Falls is maybe a mile from the road to the lower falls viewpoint? Bridal Veil is less than that. The Meadow has a boardwalk right next to the parking lot.
You can view Sequoia's in Mariposa Grove on the southern part of Yosemite or if you have time you could go to Grant's Grove in Kings Canyon or Sequoia. Kings Canyon is a much easier drive in my opinion. The catch is I can't think of campgrounds on 41 south of Yosmite other than the one I mentioned by Wawona. There is a town called Coarsegold. I would google that and see if there are campgrounds there.
