We've been to those parks multiple times - have hiked the Teton Crest Trail, have done three backpacking trips in the Wind River Range, various dayhikes/sightseeing around the Tetons, Yellowstone, and Beartooth Mountains.
As for adding on the Wind River Range, you could swing a short trip. Two options:
1. Hike into Big Sandy Lake and camp two nights with a dayhike to ******* Pass/Cirque of the towers. We did this as part of a trip when our daughter was five - totally doable (
Wind River 2012
Day 1: Big Sandy Trailhead to Big Sandy Lake (~ 5-6 miles, 610 feet elevation gain)
Day 2: Day hike to ******* Pass (~ 5.5-6 miles, 1110 feet elevation gain)
Day 3: Return to trailhead
2. Hike to Titcomb Basin. It's about 14 miles in with campsites along the way, so can break up the hike in (Island Lake is great, although crowded, and that is maybe 12 miles). There is not a lot of elevation gain though, so it's not too bad hiking in. You could maybe do it as two night trip if camp at Island Lake and day hike to Titcomb, or to make less mileage per day, could do three nights. Titcomb Basin is popular, but the basin itself is pretty large and it's easy to find a campsite with some solitude (we've camped there twice:
Wind River 2013 and
Wind River 2011).
We loved all the thermal features in Yellowstone. I know you said you were camping, but it's also nice to stay in the Old Faithful cabins if you can snag a cancellation (they aren't too expensive - they are a cabin with just beds/sink and a communal bathroom/shower house). The best part is it's literally a five minute walk from Old Faithful and you can watch it erupt when nobody else is around if you go at night. One of my favorite geysers in that area is Castle Geyser, which erupts roughly every twelve hours and if you can catch it at night or early morning, it's pretty awesome and easy to do if you are staying nearby. We've spent a lot of time in this area doing what we like to call the "Geyser Grand Slam". In the visitor center you can buy a small pamphlet (if they still have them for a quarter or whatever it was, I think there might be an app now) and write down their predicted eruption times and windows for the geyser in that area, then see if you can hit all the eruptions. The best is to watch for the "geyser gazers" with their red jackets/bikes/chairs because if you see them hustling somewhere, you best follow. It's the best way to see Grand Geyser erupt because it has the largest eruption window and if you follow them, you know an eruption is imminent.
Pictures/trip reports with geyser stuff:
Yellowstone 2011,
Yellowstone 2012, and
Yellowstone 2013
I would also recommend a hike to the Washburn fire tower. Big horn sheep sometimes hang out there and we saw a herd of them at the summit when we went. It's also a nice fire tower with great views.
We really liked the Yellowstone Treasures book for planning and traveling in the park. For Yellowstone especially I would recommend a small cooler you can take with you for the day so you can eat where/when you want and avoid the mediocre, over priced food in the overcrowded cafeterias. The Treasures book is a good with listing picnic areas, mileage, etc. for all the roads.
If you get tired of the crowds in the Tetons and Yellowstone, head to the Beartooth Mountains outside the northeast entrance of Yellowstone. There are some nice hikes and drives that way with only a fraction of the people. Have bear spray.
Really, I am serious about that.
