Here are my thoughts:
Your Grand Tetons time looks fine.
8/23 - Allow some extra drive time as there will be road construction on Yellowstone's South Entrance road. The park website is saying up to 30 minute delays (which is what they usually say and this is usually correct) while they construct a new bridge near the Lewis Lake Campground.
8/24 - The main predictable geysers are in the Upper Basin around Old Faithful which is accessed on foot. The Twilight tour drives from Old Faithful usually up to Fountain Flat Drive stopping at maybe Black Sand Basin, perhaps Midway Geyser Basin and Fountain Paint Pot. Sometimes it does a drive thru of Firehole Lake Drive. That road is pretty awful as it's gravel and broken pavement thru a thermal area. It may or may not be open when you are there. There is an excellent predictable geyser, Great Fountain, on this side road which is awesome to watch but you can drive there on your own.. So...to me you are not seeing the big geysers on this tour, they are better seen on foot from either the paved path or the boardwalks thru the basin. You will probably get good information about the thermal areas. I suggest you download the app GeyserTimes and track the predicted eruption times on there. I particularly enjoy Grand Geyser and Riverside Geyser. Daisy is good too and goes pretty frequently (every 3 hour or so).
8/25 - I'd probably not do an evening wildlife tour in August. It will have been hot during the day and many of the bigger critters will have moved up in elevation. Staying at Canyon gives you a great opportunity to get to the overlooks of the Upper and Lower Falls before crowds or after the day visitors have left.
8/26 - This sounds good. You could go do Norris Geyser Basin earlier in the AM if you want to. To me Norris always feels hot and it is just not tolerable for me in the afternoon if it's hot. I prefer to get there early AM! Roosevelt is one of my favorite locations. Be sure to have a drink on the porch of the lodge. The rocking chairs are relaxing, haha! I recommend the Lamar Sunrise drink...or is it Sunset?? haha...one does me in.
8/27 - I WOULD do the wildlife tour in the AM from here! The cooler morning means more things may be stirring.
8/28 - This looks good. If you need fuel, gas up at the Tower Service Station right there at Roosevelt. The gas stations in Cooke City are usually more expensive than even in-park gas. Take your time over Beartooth. If you want lunch, I enjoy the Red Box Car which is one of the first things you'll come to. It's right beside Rock Creek and a nice rustic setting for a good handmade burger and shake. Where are you staying in Billings? Many like the C'mon Inn which has a small waterpark inside.
8/29 - Yes, Little Bighorn is only about an hour south of Billings.
Sounds like an awesome vacation!
Here is a link to the road construction projects for this summer. Road construction is ongoing. In Wyoming/Montana/Idaho the joke is there are just 2 seasons, winter and road construction.
https://www.nps.gov/yell/planyourvisit/parkroads.htm
They have just started clearing Beartooth Highway. The Montana DOT plow drivers do an awesome job AND do videos for YouTube. They are just great to watch!
https://www.youtube.com/playlist?list=PLxseor6I1x1EpKa-KrE1KZZD8BuTSCNYk
Do be sure you stop at the Visitor Center in Grand Tetons and several of the VC's in Yellowstone to get the Jr Ranger workbooks. There is also a separate Young Scientist workbook for the Old Faithful area. I think they are $3/each.
https://www.nps.gov/yell/learn/kidsyouth/index.htm
editing to add: There is no Visitor Center at Roosevelt so get the kids to finish their Jr Ranger workbooks before they leave Canyon or you will have to go over to Mammoth to turn them in so the kids can get sworn in.
