Olivia's rage ( spoilers)

I agree this film is well-made but I saw it years after I first read the book and was disappointed at the changes to the plot which obscured the reasons for Olivia's deadly rage. There were three targets of her rage:

1) her mother, for killing her
2) her former playmates, for tattling on her
3) Magnus (her biological father) for not acknowledging her as his child

The third reason is why she wants to kill anyone who has a connection to Magnus, ie Julia and Mark (Mark is Magnus and Lily's half-brother). By the end of the book, Julia, her mother and most of her playmates are dead, and we are left to believe that she plans on killing Lily and Magnus next. The plot changes in the film make it confusing as to why Olivia wants Julia, Mark and Magnus dead and there's no reason given except that she's evil.

The Magnus in the book is also a much nastier person, and there's a suggestion that Olivia inherited her evil nature from him. The difference being that Magnus always got his own way and was never thwarted, while Olivia was thwarted by her mother killing her, so she is much worse.