NDgal: My suggestion would be to ask yourself, honestly, if there are times where you occasionally give in to your DD's tantrums in order to pacify her. This teaches a child that tantrums can be an effective tool. The next time they try it, and it doesn't work... confusion. "Hmmm... maybe I need to try harder?"
It's easy as a parent to reward negative behavior and not even notice you're doing it. Conversely, it's quite taxing to stop and think, "What is my child learning from this?" with every interaction.
The thing that suggests to me that this is a conscious strategy on her part, and not a result of some embedded personality trait/psychological issue, is that she does not exhibit this negative behavior when you're not around. My DW and I have seen this in children who spend time with us. Just one example, my niece did not run away from us in parking lots at 4yo, because we refused to chase her, so we were no fun. If her mom was with us, different story.
If this is the case, then the solution is that a tantrum must never, ever, ever result in the desired outcome, even if that outcome was something you were already predisposed to give her before the tantrum started. In fact, those situations can be the most instructive. "Well, I was going to give you that, but that was before you started throwing a fit..."
