Well, I do think some kids are more naturally sensitive than others. But, another thought: Do you think she says these things to get the desired reaction from you? She sees that everytime she talks about deer hunting or hating cats, (whether or not she really understands what these things involve) you get upset. It's probably one of the few ways she feel she has power over her older sister, and she enjoys the teasing "game." It's sort of like the sibling who takes delight in devising plots to scare the other, or the toddler who chases his spider-hating mom around with rubber spiders.
Even so, though, there's no excuse for hitting the family pets. It hurts and annoys the animals, and sets her up for bites or scratches. If she won't listen to you, try talking to other members of your family to keep their eyes out for, and correct, cruel treatment.
slops, gloops, and gruels.