Congrats to your daughter on her strong record. She sounds like a real gem, and I would be so proud!
I agree with those above who suggest substituting University of Minnesota for Madison. Like Madison, the Twin Cities (Minneapolis-St. Paul) is a great place to study poly sci because it is a state capital with lots of internship availability. UMN also has longstanding ties to China. Even during the darkest depths of the Cold War, UMN kept alive a thriving academic exchange program with a couple of Chinese universities. This is reflected even today in the strength of its Chinese program. And unlike Madison, UMN has some merit opportunities. You still might not get the price low enough, but at least you have a chance.
If she keeps up her Chinese studies, don’t forget to encourage your daughter to apply for a critical language fellowship. These are quite prestigious: https://clscholarship.org/
I agree with those who suggest considering the opportunities available through National Student Exchange if she happens to land at Oklahoma State (sadly, University of Oklahoma doesn’t participate.) NSE allows up to a full year of exchange at any of the other participating schools, paying no more tuition than what the student is paying at the home institution. Some fun schools participate including a number that offer poly sci + mandarin including: American University, St. Olaf, UMN, University of New Hampshire, Umass-Amherst, Umass Boston, CUNY Queens (NYC). Between a year doing NSE and perhaps a semester doing study abroad, your daughter would be getting out of Oklahoma a lot, while still saving a lot of money.
https://nse.org/exchange/find-campus/
Best wishes to your terrific daughter and to your whole family!