Teenagers are difficult to get a grasp on.  Do you remember being a teen yourself?   It's a confusing time and living with two people who don't seem to understand where you're coming from and what you're going through seems to make it more difficult.  Just as you're not the only parent to quarrel with their kid, your child is also not the first to threaten to move out. 

If it's getting to the point where her threats are looking real and you want to keep her safe and sound under your watch, there are a few things you need to do.  First and foremost, I assume that because you've reached out to me you are legitimately concerned about your child's wellbeing and will do what it takes to keep her under your watch.  It also sounds like you probably don't sit down with her enough to have mother-daughter talks.  There are ways to talk with your children without having it come to blows.  When parents and kids argue it's usually because certain subjects come up in passing, like over dinner, and one party is caught off-guard.  When you're faced with a question like "I want to stay out past curfew tonight" you don't have time to think your answer through.  Usually a simple "no" comes out leading to your children screaming "but why?" thus, an argument arises quickly and rather easily.  When you sit down with your daughter and anticipate some of her questions, your answers become easier to tackle giving her a better understanding of your decision.  Kids are never going to like what you have to say but half the battle is just listening to them.  Believe it or not kids do want boundaries and they understand it's your job as a parent to enforce them.  Explain to her why certain rules are in place and listen to her in return. 

I also think you need to ask her that beyond the yelling matches, why would she prefer to live with her aunt over you.  Find out the reason and compromise with her on a few things, because if her aunt agrees to take her in, you might actually lose her.  Although at least you'd be losing her to a family member, as opposed to the streets or other teens.  The fact that she wants to run to her aunt reinforces the fact that she wants to live under set rules.  For some reason, she finds you and your husband unbearable to live with.  You need to get to the root of that problem because once a child gains emancipation, you will no longer have any legal control over her life.  More children than you think go through with this and if she has the support of another family member, it will become even easier for her to carry it through.  But, we both know she probably doesn't want it to go that far.  Like most teen girls, they just want their mother's love and support through all their changes.  Sometimes, these threats are a way of waking us up to what's really going on. Consider yourself shaken and now act before it's too late because your daughter seems to need you.