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

Your daughter’s best bet would be two years of community college and then transfer to your state flagship. If your daughter intends to live in the US, then this course of action would give her a much better chance of getting into law school.

With respect to your daughter’s language skills–it sounds like she understands and speaks to you in Slovak. My son-in-law, who was born in Russia and immigrated to NY when he was 6, spent his junior year at a university in St Petersburg. It was a struggle–conversing with Mom and Dad and family members was the extent of his Russian fluency (he went to elementary/high school in NY and then to Tufts for college). He was not equipped with the academic language or writing skills he needed. It was a real challenge for him.

It was not clear from what you posted whether all of the coursework in Slovakia was in English or just some of the courses.

I would second the recommendations above that your daughter self-study and take the AP exams in May. She can travel afterwards.