You could tell the twins were interested in each other's education and wondering why it was different, then the "princess" is apparently killed. The current prince being insecure about a lot of stuff, like her(assuming it is a the princess) identity and role makes me believe it is the princess too.
Who knows, though? They keep saying "secret this" and "secret that", so it could something entirely unrelated to the gender of the current princess or just that she is female and that revealing that will not help her inherit the throne at all.