I don't think Anna's two year old stage was so terrible. She wasn't very contrary, generally followed directions and was a pretty happy child all around. The main issue we had with her two year old year was her sleeping - she continued to have night terrors - and totally random screaming and occasional tantrums.
Now, thankfully, her behavior is much improved. We have few tantrums with her - and now if she has one, it's generally "for a cause" not just because she happens to feel like throwing a tantrum. We've practically eliminated the random screaming - which if you imagine the loudest child screaming, I'd bet you a nickel she was louder. And she really doesn't have night terrors and is generally sleeping through the night (although she still has the occasional
nightmare, as I believe all kids do).
But now, as Anna is just a bit over three-and-a-half, she's got an attitude. I don't mean she's like this all the time, but she's picked certain things to be obsessive about to no end - like she MUST be the first one down the stairs. I MUST put her in the car first and she MUST be the first one taken out of the car. With other things she tends not to care, but if she doesn't get her way on these issues, she will either throw a tantrum or hold a silent, pouting sit-in (reminiscent of the 1960's era protesting).
Or, if I ask her to do a perfectly logical (and easy task) like cleaning up two toys from her room, sometimes she will decide that she wants no part of that and declares that she doesn't know how. If we are in the middle of walking somewhere and she's in a bad mood, and has decided not to walk anymore, we are suddenly back to requests to be carried and she says that her legs are broken (this - by the way, started long before the new baby arrived, so I highly doubt it's connected).
90% of the time, Anna's an angel. But the other 10%, I'd say she's earning her certificate as an official three year old.