Tantrum twos?

OK, so we're not the first parents in the world with a two year old. We're not even the first parents to have a two year old, who is independent, feisty, refuses to admit to having pookie nappies, only wants to feed herself unless she's too tired, and will NOT let you take bandaids off (and for some reason on M they are really sticky. I wish regular bandaids stuck to me like that, I wouldn't need my lifetime's supply of Elastoplast).
I think we had four or five tantrums before we left the house this morning, and that was early because I had a 7:30 meeting. Something terrible happened with Daddy in the kitchen while I was getting ready. Then something else cataclysmic happened over breakfast. After brekky, M played with some pencils Mumma had left on the kitchen bench the night before (doh!). There was a fair amount of coercion involved in getting her into the bathroom to brush her teeth. The pencils came too. Miss M was determined to touch the pencils after brushing her teeth ... but *before* she wiped her hands and mouth. Cue tantrum #3 (not sure how ignoring her in this scenario get her mouth wiped and tantrum stopped??). Number 4 was about getting into the car. And then another one upon getting out of the car.
Sometimes, during the tantrum, I can quiet her down by telling her to sit in the corner and calm down. This seems to be a Fate Worse Than Death, so M generally calms down. She then wants a kuggle (latest pronounciation of cuddle). We're probably not particularly strict about *not* giving a cuddle, and should be (but she's asking for a cuddle, and normally she won't stop long enough to let you kiss her cheek, let alone a real head tucked into the shoulder cuddle).
The escalation from "I'm not getting what I want" to screaming like a limb has been severed is what's shocking us the most.
I keep on telling myself that in the midst of the tantrums and yelling, we are experiencing some Terrific Twos, not just Terrible Tantrum Twos. ;)