Philadelphia to Yellowstone

We're looking to plan a 16 day road trip from Philly to Yellowstone, and back with 3 pre-teen children (9-12 yrs) near the end of August. The kids know they would like to go to Wrigley field in Chicago, Mount Rushmore, and see Old Faithful, but we're not sure what else would be good to see for kids in this age group.
On the way towards Yellowstone it looks like we drive through PA, OH, IN, IL WI, and South Dakota.
We're staying in Yellowstone for 2 nights, and around the Grand Tetons for 1 night.
On the way back we're thinking about going through Colorado, Kansas or Nebraska, Missouri (St. Louis Arch).

We have a several questions if anyone can help.

Would you recommend going into Chicago beyond just trying to see a Cubs game if they are in town?

What type of driving speeds or distances are typical through the mountain areas, such as around Yellowstone park?

Any suggested routes, side trips, or other ideas? Anything in Montana?

Thanks.

Chicago? Absolutely! I'm not sure there's another city in the United States that is MORE interesting although many others are equal to it. Cruise around the downtown, along the lakefront, visit the planetarium or perhaps one of the great museums.

In mountain areas, especially at the higher altitudes common in the Rocky Mountain states, you can expect driving speeds on two-lane highways that average about 45 mph. Some highways will flow faster in the more open areas, and of course the interstates are made for higher average speeds, but you get the idea.

In Montana, I wouldn't miss the Little Bighorn Battlefield and Pompey's Pillar. For scenic beauty, you can't beat anything in western Montana -- anywhere. Also, around the Black Hills, there are many, many things to see besides Mt Rushmore -- Custer State Park, Wall Drug, Badlands National Park, Crazy Horse Memorial, Lead-Deadwood, Sturgis (depending on your dates, the motorcycle rally in Sturgis could clog things up a bit).

Thanks for your insights. Our preliminary plan is outlined below. Does this seem practical?

Day 1: travel as close to Chicago as time allows.
Day 2: Into Chicago for most of the day.
Day 3: In Chicago. Chicago overnight.
Day 4: Driving through Minnesota. Stay overnight near western part of MN or just into South Dakota.
Day 5: Drive through Badlands NP, Visit Wall Drug, overnight around Rapid City. Perhaps visit Mt. Rushmore at night.
Day 6: Rushmore, Crazy Horse, Custer State Park area, then drive towards Devils Tower. Overnight near Devils Tower.
Day 7: Devils Tower, drive towards Little Bighorn/Pompey's Pillar. Overnight near Billings, MT to Cody, WY.
Day 8: Drive into Yellowstone. Overnight at Yellowstone.
Day 9: In Yellowstone. Overnight at Yellowstone.
Day 10: Through yellowstone into Grand Teton area. Overnight in Grand Teton area.
Day 11: Drive towards Rocky Mtn National Park. Overnight between Cheyenne, WY and Rocky Mtn NP.
Day 12: Around Rocky Mtns, then drive through Denver and overnight somewhere in the western part of Kansas.
Day 13: Drive through Kansas, perhaps overnight near Kansas City, MO.
Day 14: Drive by St. Louis arch, perhaps then on to Mammoth Cave in Kentucky.
Day 15: Visit Mammoth Cave, then start the trek back to Philadelphia.

Thanks again.

It seems do-able to me. If you happen to pass Chamberlain, SD at lunch time, you might consider stopping at Al's Oasis for a buffalo burger! It's just beyond the Missouri River bridge, if I remember correctly. Bob