I'd compromise if I were you since she is not in school. Here's what you do. Tell her that she has a midnight curfew 7 days a week IF she goes in with you and gets depo provera shots every 3 months. Tell her that you are not interested in becoming a grandmother now, and teens notoriously get pregnant even when they think they are being "safe".
You aren't going to keep her from being sexually active - that ship has probably sailed anyway, so it's a matter of keeping her from getting pregnant. Tell the doctor to talk to her about STD's since she doesn't want to hear it from you. (You can go online and copy pictures of the WORST looking STD's imaginable - graphic stuff, mom, and give the doctor the pics to show her, without her knowing that they come from you!) This way, perhaps she'll insist on condoms to prevent STD's in addition to having the shots.
Yes, you should still demand that she do household chores.
I really think that you should let her go once she turns 18. Start now working with her to figure out her budget living on her own, including health insurance. Find out if she can be under your insurance. She's not a student - can she indeed be covered under you? (Sorry, I don't know...)
Sometimes a kid like yours just needs a kick in the pants outside of the nest to understand the facts of life. Maybe getting a sober view of life with a GED and life in fast food without the comfort of your home will make her decide that she wants to regroup, come home and actually go to college. If you try to keep her at home, she won't figure it out.
By the way, both my kids, who don't have your daughter's issues, have midnight curfews, and my younger son is 17 and in high school. So what I'm suggesting is not out of the realm of reason. However, since she wants this so much, I'd DEFINITELY demand tit for tat to get her birth control that YOU can count on...(I doubt she'd remember to take her BC pill and you don't want to have to harp on her every day over THAT!)