I can't afford to send my kid to a good uni in the USA, so are European universities alternatives?

^ but this a small outfit that wouldn’t really be recognized for law school purpose.
For ease of transfer back to the US, the university needs to be recognizable to us institutions, IE, ancient, among the top 3-4 Slovakia.

The priority should be, first, the PSAT, and, second, preparing for 3 AP exams. Taking foreign language subject tests and any other subject test demonstrating mastery will be necessary since she’s been homeschooled.

This student’s best chance is scores demonstrating excellence in some subjects (subject tests, AP) as well as a high SAT/act score, leading to a good scholarship from UTK or UTC or admission to a meet-need school that will be interested in her profile.