Before I add 3 hike choices for each location I agree on possibly adding a water day. Scenic floats are great, but IMO the River has simply become too crowded. How about renting canoes and doing a long day or easy overnight to Leigh Lake? Not many easier portages to a lake full of jaw dropping views with great permitted campsites?
Day 1: Do the Falls and Rim Trails: Easy, and as crowded as it might be Yellowstone’s Canyon is pretty darn spectacular. Kids [Ages?] will love the Brink of the Falls. Do some games or something later in the day. I’m 47 and I’ve liked just about every Ranger Program I’ve seen in recent years, and kids seem to really like them. Cool after dinner thing.
Day 2: Kids should see Yellowstone, and you should drive the loop. Road wildlife is thrilling for lots of us, and there are any number of things to choose to see. Personally I think the waterfalls in the Canyon and Cascade Corner are Yellowstone’s great treasures, but most of us and particularly kids like Geysers. Old Faithfull will simply be crowded and the most densely populated of all park days. Sometimes a parent has to do what a parent has to do. Make stops, get some more exercise.
Day 3: Avalanche Peak. Get out good and early and avoid storms and set on one of the great summits of all of the Rockies. It has a truly exquisite view, immense and including the Tetons and the days ahead. Unless kids are super small this is done by lots of families in a relatively short day. Short but a good vertical.
Day 4: If the drive down after Avalanche isn’t too late get up early, get over to the Marina and hike Hermitage Point past the popular Swan Lake and Herron Pond 3.2 mile loop. The farther you get out on the Peninsula the wilder it gets. Early morning or evening canoeing can sometimes be very cool, so if you were to give up the Campground for a night you could get a group [free as walkup when available which I’ve found to be surprisingly often] Permit to camp at the only site on the entire peninsula. Some could hike, some could canoe. Make it an evening dusk hike and wildlife is as good as the Lamar IMHO. The Views of Moran and the Tetons are incredibly rewarding.
Day 5: Assuming you don’t overnight Hermitage Point instead of Wyoming’s most popular hiking trail I suggest you go another canyon or lake. I did most of the classic/major alpine lakes in the Tetons by the time I was 12, and I was tiny until my sophomore year of high school. Although I’ve been with 8 year olds to Lake of the Crags I can’t recommend it since the trail is not sanctioned/maintained by the park service. Ampitheatre is longer. If kids are younger Bradley and Taggart are Spectacular.
Day 6: Taking the Tram up to the top of Rendezvous is pretty darn cool for kids of any age. IMO then hiking 11 miles down Granite Canyon is darn cool too. Have dinner in either Teton Village or Dornan’s or Signal Mountain Lodge on the way home.
Day 6 option: For much of the day you could a) go to Jackson, b) Do the boat across Jenny Lake and see the falls, perhaps Inspiration Point.
Later in the day drive to Mount Leidy Trailhead in Bridger Teton National Forest East of Moran. Depending on how fast you’re willing to drive a 15 mile Forest Road perhaps an hour for most of us from trailhead to Colter Bay afterwards. This is dense Grizzly Habitat, so stick to the protocols you should have observed throughout your trip. Arguably the best view of the entire Teton Range. This hike is 1.2 miles, about 1,200’ vertical. Depending on where you’re headed there is some great camping much closer to here I’m willing to tell you about privately. With Avalanche Peak and Mount Leidy the children of every age in your party will take in a truly wonderful swath of the American West and will not kill you for force marching them without taking in more of the kid stuff of all ages in the area.
Whatever you do have a wonderful trip.