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

If she does well enough on the PSAT for National Merit, there may be some full ride scholarship opportunities based on that:
http://nmfscholarships.yolasite.com/ (verify on school web sites)

There may be other full ride scholarship opportunities (not National Merit based) to look into (again verify on school web sites):
http://talk.qa.collegeconfidential.com/discussion/comment/20798968/#Comment_20798968
http://competitivefulltuition.yolasite.com/