From what you describe your cat doesn't hate you!

She is playing as she would with litter mates and expressing very natural behaviours such as hunting and stalking.

You could try taking her by suprise and roll a ball, a ball of wool or a foil ball into the room before you enter it. She can then "hunt" the toy and not you. She will also begin to associate you with the toys rather than you being the toy.
Set aside some special time to play with her every day and look into getting her some things to keep her occupied during the day - one of the best toys I've found is the kind that has a track with a ball on it that the cat can chase and hunt without getting it out. If you can get a selction of good toys and leave out a couple of different ones every few days this will keep her interested. Keep a really favourite one as the one she only plays with when you are playing too.