literally: really, actually, without exaggeration
hateful: unpleasant, deserving hatred

Please see the note below from www.answers.com :

For more than a hundred years, critics have remarked on the incoherency of using literally in a way that suggests the exact opposite of its primary sense of “in a manner that accords with the literal sense of the words.” In 1926, for example, H.W. Fowler cited the example “The 300,000 Unionists … will be literally thrown to the wolves.” The practice does not stem from a change in the meaning of literally itself—if it did, the word would long since have come to mean “virtually” or “figuratively”—but from a natural tendency to use the word as a general intensive, as in They had literally no help from the government on the project, where no contrast with the figurative sense of the words is intended.

Even though "hateful" can have either meaning (according to Webster's 10th New Collegiate), it is most commonly used in the sense of "evil, deserving of or arousing hate." In this text, one sister is saying that the other is "hateful" in the more literal sense: "full of hate."

First, I think the usual sense in which "hateful" is used is the one less justified by the etymology: something along the lines of revolting, awful, repugnant,.... There was a time when upper-class English girls would describe anything they found vaguely displeasing as "hateful", snails, the clothes their mothers made them wear....

The literal sense of "hateful" is, of course, "full of hate", and I think what is happening here is that the girl is (more or less automatically) thinking of her sister as "hateful", and then this word provokes a kind of a transition, so that she realises (or comes to think) that the reason that her sister is behaving in this "hateful" (i.e. unpleasant) way is that she is, literally, "full of hate".