According to his own account, Frederic-Auguste Bartholdi, the sculptor

Hey Rath's - you're absolutely correct that the possessive "mother's" refers to the face, so A would be correct were it not for the meaning of "modeled like" vs. "modeled after". "Modeled like" means that he did the modeling in a way that the mother's face would have, and that's not a logical meaning. "Modeled after" means that he made the face look like that of the mother's.

I hate saying that it's an idiomatic thing because it's really more of a meaning issue, but I do think that it's one of those questions that may have been fair 10-15 years ago when it was an American test but that may not be all that fair in the >50%-of-tests-taken-outside-the-US days. I just don't know how common it is for international students to note that particular distinction. But you should know that meaning issues are very testable, so the ideology behind that question is definitely fair game.