That sounds like a good trip, well apportioned between those areas.
I've got lots of suggestions about Yosemite but not a lot of details that will help you take advantage. For example, I like going up to the overlook on the south side of the park, but I don't know what it's called or how to get there.
Also, when driving in through the main entrance. Go ahead and stop along the one way road where everybody else is stopping, and if you go too far consider taking 10-15 minutes to go back around or come there later. Do it near sunset if you can. That image is #1 on the list of the most beautiful and amazing images I've ever seen.
We have enjoyed biking around the main Yosemite Valley area, mostly towards Mirror Lake (you can rent bikes). This is a pretty easy ride and a way to get around without driving. It was easy enough for our 4 year old to do on her balance bike (except for one small overpass that was scary because she zoomed down it and couldn't stop). There are probably more advanced bike trails if your kids can handle it.
I don't know how much water the waterfalls will have, we always go in late summer or fall when Yosemite Falls is dry. There's Bridal Veil falls (I think) which is nice and usually has at least some water and has a decent hike that kids can handle.
There are plenty of other trails you can research, I'm sure you can get good information about which are best, but we haven't done many recently enough for me to recall.
I like Yosemite itself much better than the Sequoia National Forest, although it's not really a fair comparison. Sequoia might be nice if you just want to camp rather than "sight-see in nature". When we stayed there we spent a day doing sequoia specific stuff and the rest of time was just camping. My wife disagrees, though, telling me there were plenty of things she wants to go back and do. So... I'm no help.
Oh, but she did second the biking thing.
