I'm a native St Louisian who now lives in Allen, TX, so I'm extremely familiar with the 2 routes. One route takes Hwy 35, while the other takes Hwy 75. Take Hwy 75 which is much more scenic. Along the way, there are lots of things to see while driving in the car...nature type things and small roadside shops along the way. Rather eclectic & townie. Hwy 35 is pretty much just highway. You'll go thru Tulsa which has lots to see by itself. Between Tulsa & Springfield, MO, there's the famous McDonald's over-the-highway...a must see for all! Kinda cool, really. Then there's Springfield, MO...historic. There are small towns just off Hwy 44 with touristy things that your daughter might like. And, of course, St Louis is filled with things to see and do.
Do some Google searches & you'll find plenty! (i.e. Tulsa, OK attractions) Here are a few sites:
www.springfieldmo.org, www.explorebranson.com, and /www.roadsideamerica.com/story/11683 (McDonald's).
NOTE: Lake of the Ozarks is nowhere near your route.
Good luck! And I hope you enjoy the ride!