Whiney toddlers?

I have a terrible two year old and a frightening four year old. The oldest is the most baffling. She's smart, funny, beautiful and totally infuriating! She randomly refuses to do things we ask of her, digressing into some sort of crazy madwoman, complete with tears, wails, throwing and kicking. She's moody, one minute saying, "I love you, Mommy!" and the next she's screaming, "I hate you Mommy!" And it's all over the fact that she refuses to feed the cat or put her dish on the sink, or have me brush her hair!

Really?

And the two year old just thinks it's normal, so she starts doing the same thing.

But the worst is the whining. At the faintest hint she's not going to get what she wants, she starts wimpering and protesting, as her little fair face crumples. It's not like she gets what she wants when this happens, so why does she keep doing it? I know she's only four (and a half), but it just seems so immature. And it's driving me batty!