She's 17. I would do what Florence and ktf suggested and find her an inpatient program. If your local hospital has a mental health helpline, you could call them and tell them what you're dealing with and ask their advice. I don't know what the drill is for inpatient rehab for alcohol abuse; I know that for many mental health programs, they won't take a kid who is not agreeing to being hospitalized.
I know it is terrifying to admit to yourself that your child has a problem you can't solve for them, and that you're dealing with something that's way above your pay grade as a parent. And that you missed it. I've seen it in my house. I've seen it in my friends' houses. There are a lot of hurting teen girls today, in a way that didn't happen 30 years ago when I was in high school.
I had to admit my 13-year-old to a mental hospital a little over a year ago. That was a different situation -- she was self-injuring and suicidal -- but some of it, i think, is similar for a mother. The most important thing for you to remember is that you didn't cause this, and it's not because you're an awful parent that she's drinking. There may be underlying mental health issues, there may be normal teen angst, she may just be one of those people who for whatever reason starts drinking and develops an addiction.
None of it is your fault.
But you may be in a situation where, just like I had to, you have to make the choice to remove her from the home to a context where she can get serious help -- not just for her sake, but also to protect her little sisters. That was the last drop for me, when I realized her little sister wasn't safe around her.
Oh -- and when you talk to her, I wouldn't blame or punish. I would tell her that you are extremely concerned about her and that you want to get her help. But I think I would get some professional advice on how to approach it -- if nothing else, an emergency appointment with a mental health professional...