I'm 47, I have two teenage daugthers (17, 14) and a son who's almost 12. Life with hormonal ragings can be CRAZY and there doesn't seem to be any easy or quick way to simply make it all 100% okay. But what I have found through much trial and error is that there are a few real basic principles to adhere to: Let her know that her feelings are valid because there are HERS right now, and she can DISCUSS or share anything with you as long as it is with a respectful attitude, BUT that no matter how she feels, she WILL NOT vent poison on you or her brother (or anyone else, for that matter). Yes, she has huge emotional swings, and if she needs to cry in her room or go for a run, or write it out, that's all legitimate -- but if she begins to torment the rest of the family (which she is very capable of!), then there will be repercussions. Clear repercussions. As in, write it down and show it to her repercussions. As in You Will Lose Priveleges repercussions. When it is written down (i.e. being disrespectful to your mother will result in losing your cell phone for a day, or no friends over Friday night, or whatever it is), you can more CALMLY stick to your guns about it. A real big thing I've discovered is to (try to) NEVER let your self get emotionally pulled into it. Almost impossible to do, but when you have it all written out, at least you can just point to it and say, okay, this is the consequence; sometimes it's easier not to get pulled into a big emotional scene that way. Teenage girls are MADE to push buttons. Oh, and when you write all this stuff down, it's a good idea to actually sit down and talk with her (in one of the less hormonal moments), and go through it, discuss expectations, repercussions, remind her that you know this is a really tough time and it will pass at some point, and you're in her corner and even though she doesn't think she wants it, she really needs you to be the mom right now, and that is EXACTLY what you're doing because you love her and you want her to be ready to go out on her own and be fully happy when she does so!
Beyond that, be really good to yourself. Don't beat yourself up, remember pretty much 98% of the mothers of teenage daughters out there are experiencing the SAME THING, and try to keep a sense of humor!! Laugh (by yourself) at the whole situation... Go out with the girls... Go get a manicure or a massage or buy yourself flowers. And realize that even though you don't deserve it, you are receiving the brunt of some serious emotional upheaval right now, and you need to take care of yourself in other ways!
This, too, shall pass!!!
Good luck!