I won't be much help and will sound as though I'm telling how to be a good parent. Not so. I'm sure you are a good parent.
As I see it (and this is not just about HP & the theater conundrum), you have to assert your authority at all times, but you can't "win" all the time, if that makes any sense to you. With each "head-butting" situation, either you reach a compromise or one of you "wins" and one "loses". It's very important that you choose wisely which ones to win, so as not to crush her self-esteem or push her to the point where she will be rebellious. You cannot let her "play" you (i.e., are the distress & the tears genuine?) and you cannot let her win in every situation; it's a recipe for long-term disaster. If the two of you make enough of the right choices, it's a good bet that you both will survive these teen years and be great friends.