H.G.
My friend went through this. Her son went on a total drinking strike when she introduced the sippy cup. He refused to drink for FOUR days, which scared the heck out of her! But he finally gave in, when he got thirsty enough. And now he's a sippy cup man, through and through! :)
Also, I would try one skill at a time. First get her to drink out of the cup, and then work on her holding it by herself. Two skills at once is just too overwhelming!
Your daughter sounds like a pistol! Those smart, feisty girls are so much fun!
PS My son refused the sippy cup at first too, but then had no trouble when I introduced the "Nuby" brand. That's kind of halfway between bottle and sippy cup. (A little softer spout.) Now he only drinks out of the Born Free sippy cups, and just loves them. Holds them by himself and everything! Those two brands are just a little easier to get the milk out of, and don't have the same strong vacuum. Better for the ears, too!