Crystal Cave is nice, but not for kids under three. They get badly scared when the ranger turns out the light so we can all enjoy total blackness. Ask how I know this.
Great year for Sequoia -- lots of snowmelt! If the kids are old enough to walk a few miles, Tokopah Falls is amazing. And of course Giant Forest.
The hard part will be finding a vacancy in a campground -- the opening is delayed a little due to the snowpack. Dorst is nice, and so is Lodgepole.
How old are the kids, if I may ask? And how many days do you have for this part of your trip?