All I can remember is quite vague but it’s about a woman (teacher) and her younger (half?) sister who is a genius. The girl is sent to a boarding school (possibly reform school) where there are horses and snow. The woman takes a job there to keep an eye on her sister. I think they have different surnames so nobody picks up on it, except it turns out an ex boyfriend also works there.
The girl kills some of her classmates and wears a baseball cap on one occasion so that she can avoid cctv.
Any ideas?