Why Does My Daughter Have Mood Swings And Yell That She Hates Me All Of A Sudden?

Because she is 33 months old. Ignore her (don't feed her seeming unhappiness), be loving, find ways to move her physically and emotionally into other territory, be consistent. Sing to her, read to her, play with her, set up the dollies and stuffed animals in rows and dance in front of them or sing in front of them like they are your audience, play lots of pretend games, dress up in shawls and hats and daddy's old boots -- in general, have fun with her and don't play the screaming game. Be a mom.

Yep 2 year olds, normal most likely,

They don't call it the terrible two's for nothing, but if you think this is fun wait until she's five. If this keeps up I'm moving out when my kids become teenagers.:p

You have to remember that at the age of 2 your daughter is trying to gain her independence but isn't quit ready to cut the apron strings. This lashing out is her way of gaining her independence while still holding on to you. I know it's a funny way to go about it, but after all, she's only two.

Try changing the subject every time she has a fit, time out works (1 minute per year old, she's two so two minutes) try taking away privileges if she doesn't stop yelling at you, or try telling her how it hurts your feelings when she says stuff like that. Either way, good luck and don't give up, it will get better, only to get worse again when she turns 13.;)