Oh my goodness, I can't imagine placing a family in a house in Three Rivers for any length of time. If you're lucky, the kids would enjoy a few hours on the little beach there (IF it's safe at the time you're there), but they shouldn't be going in the water anyplace else and the nearby manmade-lake is, without a boat rental, not a place for recreation.
If you really want to see Sequoia or Kings Canyon, stay in the parks. Kings Canyon has housekeeping cabins (rustic) and that will be your best choice. Hume Lake may have something, but it is usually rented out to large groups and their overflow policy really varies. I suppose the Montecito-Sequoia Lodge and Family Resort might be another suggestion, but I strong advise staying in Kings Canyon cabins or other lodgings if at all possible.
Here are things in Sequoia kids like to do (we took our kids every year, usually more than once, every year from age 1 to age...current):
Beetle Rock and History Museum (and the old growth forest right next to Beetle Rock). Might see some wildlife. Kids like the Museum, it's aimed at them. There's also the Nature Center at Beetle Rock.
Moro Rock (the best "rock climbing" experience available - using stairs.
Crescent and Log Meadows (and even longer hikes in that area).
Picnicking (various places: highly recommend Crescent Meadow)
Lodgepole Creek (sandy beach near the bridge, Nature Center).
Tokopah Falls hike. Many other hikes in that area and out of Wolverton Meadow.
Little or Big Baldy Hikes.
They can pick up sticks in the area between Sequoia and Kings Canyon and practice whittling. They can even make a fishing pole and fish in Lodgepole creek (if they are very quiet, they'll see fish - they probably won't catch any; but I've seen kids catch fish when the creek at Crescent Meadow is flowing).
Grants Grove Hike and all the various wonderful hikes in Kings Canyon.
The most fun, though, is tent camping because then you may get to see bears.
It's my understanding that the roads are relatively snow free, but we need to near from WuksachiStaff about whether the road to Crescent Meadow is open (you can walk to Crescent Meadow and Tharp's log - a must see - from the General Sherman tree area, though, it's not that far).