Thanks again to everyone for the info. We ended up having a great trip. Didn't explore quite as much of GNP as we had hoped, but the hikes we did were a blast. I'll add TRs and photos one of these weeks, but for now here's a summary of what we did:
22 July our family took the boat across Swiftcurrent and Josephine Lakes, then we did the hike to Lake Grinnell, and hiked back out to the Many Glacier Hotel amidst plentiful wildflowers and wildlife (including an up-close photo-shoot w/ a moose)
23 July we hiked the Swiftcurrent Trail to Swiftcurrent Pass and then bush-whacked along and below/around the Garden Wall and up to Point 8,479, then descended, with several up-close encounters with moose. Had to wade the creek at one point, had several snow fields to deal with (one steeper one at Devil's Elbow where ice axe came in handy), but nowhere near as much snow as we would encounter in the Tetons the next week. Some fun glissading on the way down from the Garden Wall and Pass. The face below Mount Grinnell had over a dozen waterfalls cascading, most of them diving hundreds of feet. The Garden Wall hike to Point 8,479 lived up to expectations and was an awesome, awesome day with unbelievable scenery.
We got to explore most of the park's main attractions, including many of the waterfalls (Rustic, Undine, Lower, Upper, Gibbon, etc.). We saw hundreds of bison in Lamar Valley, and saw grizzly, black bear, mule deer bucks and bull elk all up close. Summit-wise we didn't do a whole lot of hiking, but the entire family did hike the 4.2 mile trail up and down Bunsen Peak. The board walks around the natural springs and geysers, and especially the Grand Prismatic Spring, were a lot of fun for everyone to do.
29 July we did the Paintbrush Canyon / Divide / Lake Solitude / Cascade Canyon Loop. Scenery was again breath-taking, and the snow was very heavy above 9,000 feet in both canyons. Ice axe and crampons were essential. To gain the divide required a half-mile-ish long ascent along a 45-degree slope, and there were numerous short stretches crossing snow slopes in north Cascade (some of them steeper than 45 deg) before reaching Lake Solitude (which was still ice covered for the most part).