Each summer I spend from around June 1 until early October at my cabin about 11 miles outside the SW corner of Yellowstone. Both parks are fantastic and are great places to take the family. I agree with everything Chewbacca said and would add a few other considerations:
(1) The Canyon visitor center is focused on the Yellowstone super-volcanoes and does a great job presenting the immensity of the eruptions compared to Mt. St. Helens. My cabin is on the side of one of the previous super-volcano calderas, so I'm always looking out the window for a pyroclastic cloud. The Old Faithful visitor center is also really good. Both centers have free films, which can be a good way to cool off on a warm afternoon.
(2) One of the highlights of Yellowstone is the wildlife. Keep in mind your best chances to see wildlife are in the very early morning hours and at dusk. The animals don't like to be exposed to the heat of the sun, except for the bison, who don't have a choice. If you do any backcountry hiking away from the crowds, take bear spray and keep it handy (not stuck in a backpack). I think I saw a place last month next to the Canyon visitor center that rents the cannisters. Otherwise they cost around $50. Either the summer of 2016 or 2017 a guy got killed and partially eaten by a mother grizzly and her two cubs a short distance from the Canyon visitors center, so, while unlikely you'll even see a grizzly in the park, the precaution is no joke. People are attacked by grizzlies in the greater Yellowstone ecosystem each year. I own "Death in Yellowstone" to scare my houseguests upon arrival, but I haven't had to read it - I just read the newspaper. In 2018 there have been two bison attacks and two elk attacks in Yellowstone (in Mammoth Hot Springs - don't walk between a cow elk and her cute baby for a better photo angle). The bears so far are being held scoreless.
(3) Traffic is going to be bad in the parks, which is another good reason to drive around very early and very late, and hike in between. Or buy some drinks at the upstairs bar at the Old Faithful Inn and watch the geyser from the upstairs deck. Although you have a pretty good outline to cover both parks in the brief time you have, I'll throw out another back-up plan, if you get sick of the hordes of tourists. The entire Yellowstone ecosystem is really pretty and has a lot to see. My property, for example, was originally slated to be part of Yellowstone NP, but economic interests (probably timber) had the proposed park boundary moved before the park was established, so there are some really nice sights near my place. So here are a few places convenient to West Yellowstone (within an hour drive), where I think you are staying, that will be away from the hordes, but worth seeing: Wade Lake and Cliff Lake (next to each other), Big Spring and the Johnny Sack Cabin, Sawtelle Peak (connects to Mt. Jefferson by a nice, alpine trail, albeit through prime grizzly country), Upper Mesa Falls (with a nice visitors center), Lower Mesa Falls, Cave Falls and Bechler Falls (these last two are actually in the SW corner of Yellowstone NP, but can only be accessed by car by driving in on a short road poking in from the SW side of the park). Some of these sights are accessed by a (US Forestry Service) gravel road, which is common up here, so don't lose your nerve when the pavement ends. If you are out west of Yellowstone, a nice restaurant/bar is located at Trouthunter located in Island Park, Idaho.
(4) The geology of this area is fascinating, so if you get a chance to attend a ranger geology talk, go check it out.
If you have any specific questions, post them here and I'll check back from time to time. I've got a group of friends and family arriving from Austin the first week of August for a visit. My copy of "Death in Yellowstone" is already on the coffee table for them.