From a purely behavioral pov, what you're doing by ignoring her is called extinction. When you ignore the behavior it will escalate, because she's upping the ante to get you to react. If you continue to ignore, eventually (the length of "eventually" being dependent upon the personality of the kid), after a nice huge extinction burst, it will go away. If you waffle, and give in even rarely, it actually further reinforces the behavior-- which is why I personally hate extinction as a b mod thing, because it's wicked hard to pull off. I like KJP's response, honestly.
