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

I would not recommend studying outside the USA if she wants to continue studies here, very surely she needs to homologate the European university title and it is very certain that they will not be worth many subjects and will have to repeat them to receive their degree.

Totally agree with @3scoutsmom
The solution is apply to State University looking for a full ride.