Is she experiencing peer-group pressure? What kind of crowd are her friends? You have your work cut out here, and very wise of you to take a step back because the first thing she (and her ma) may chuck at you is that you aren't her father.
Piercings can heal over. When she's old enough to have it done, if she wants it done, it's her choice.
Believe it or not there are families where screaming, swearing and stamping about are normal behaviour, and if your girlie is under the influence of some like this then that's where it's coming from.
But separating her from bad influences is also fraught with problems - if done directly it will drive her towards them, not away.
At 14 she can't legally stay on her own (well you can tell her that) and so she'll have to come on holiday and make the best of it.
Has mother had any meetings at school to talk about the truancy, possible causes and means of addressing? Not to late to do so.
Take heart. I recall my own DD being foul from 13-16, and suddenly becoming lovely at 17. It's just so tempting to throttle them in the difficult times. Best of luck.