I think it was explained that the Intention never hated Alice, but not what was up with what you're describing. I think she didn't hate Alice, but B-Rabbit instead. Oz the B-Rabbit is the reason that Alice committed suicide 100 years ago, as she wanted to stop Jack from hurting Oz further by using the Intention through her to give Oz more power to destroy the world. The Intention herself doesn't want to do things for Jack like she had done, but she's unable to say no to him for some reason. The Intention probably didn't hate Alice, only the power of B-Rabbit inside of her, besides I don't think the Intention hurt Alice when she first encountered her in the series - only used her as bait to draw out Oz because of Oz's connection to Jack.