Let me be a bit blunt here - the universities that are likely to give her a near full ride in the USA are not likely to be the ones that will do her a whole lot of good if she returns to Korea. Four years at Kentucky Tech or Western Vermont State University free of charge and then you return to a country which, for the most part, seems to prefer more school recognition.
Let me be even MORE blunt. In my birth country of Elbonia (somewhere in the middle of nowhere in Europe) the majority of people who go to college out of the country are those who could not get in to local colleges given our nasty entrance exam process. With her grades and test scores she should be able to get in to a decent school in her home country or I would hope she does.
I have lots of friends who came with me from my birth country, went to Kentucky Tech and WVSU type schools to keep costs down, went back to Elbonia, and basically gained no advantage from such a degree. After the first couple of waves of good school degree holders, people flooded the WVSU type schools and returned, negating any advantage. This is based on my birth country where lots of people came for school abroad and came back. I do not know anything about Korea, and the system may be different and foreign degrees, especially American, may be valuable.
A classic example - Computer Science (one of my degrees. We did not have Comp Sci so I came to the USA for a second undergrad then grad degree. In four short years, That was a guarantee of good money and the like when I started. Little did I know that in the brief time it took me to get a BS and MS degree, people with BS degrees flocked overseas, mostly to the UK, got a quick 1 year M.S. Comp Sci, came back, and had serious trouble finding a job.
These are things to consider before selling all the family assets to send kids to the USA without thinking why. It’s not like we don’t see it here of course…