I took my family on a similar trip 2 summers ago, and it was easily the best family vacation we've ever taken. My kids are teens and they absolutely loved it (as did my wife and I). We started with the Tetons for 1 full day, then spent another 2 days in Yellowstone, then 4 days in Glacier. We drove from the DFW area...what a long haul!
Ultimately, 10 days wasn't enough time for the whole trip...it should have been at least 14 days. I had never been to any of those parks, so the first time I saw the Tetons, I was in awe. Amazing mountain peaks, hiked around Jenny Lake, saw some wildlife and waterfalls, just gorgeous.
Then we got to Yellowstone, and it was the most magnificent place I had ever seen. We were there for 2 days, but really wish we had taken the time to stay just one more, maybe two. The wide, sweeping views were simply beautiful, and there are tons of wildlife (which makes driving around the park difficult for multiple reasons). It literally took 2.5 hours to get out of the park because of the people stopping to look at a couple of elk on the side of the road (right by signs that say don't stop).
THEN we made it to Glacier, and, well, it was just the icing on the cake. It was amazing! I didn't think anything would top Yellowstone until we drove across the park on the Going To The Sun Road. The views are breath-taking. And even more curious, is that Glacier is in a sort of convergence zone of 5 different climate types. We hiked to Bear Hat Mountain in the snow on the Fourth of July!
Days are LONG that far north. I think it was actually finally dark after 10pm, and the sun was lighting up the sky around 4:45am.
We went on several hikes, some short, like 1-2 miles, others around 8-10 miles. Seeing the waterfalls, rivers, and glacier-fed lakes in GNP was the absolute best.