Let me preface this by saying that I've been called a cold-hearted bitch by more than one person. I prefer the term pragmatic.
I will also say that I'm talking from some family experience here.
This all sounds like a Dr. Phil episode. It may sound harsh, but you may have to throw her out. It may be the best thing for everyone concerned. You CANNOT allow her to run your lives and even though tough love probably hurts you more than her, you may have to practice some.
You and your GF should sit down together and develop a set of house rules. Determine exactly what and how much you are willing to give her and then stick to it. Present that information to her. She's obviously smart so she'll get it. She's also obviously manipulative and knows how to play people. Don't let her play you.
Tell her in no uncertain terms that once she turns 18, these are the rules that she will have to live by if she wants to stay in your house. If she doesn't, these are the consequences. Then enforce both. If you don't enforce your rules, you are just enabling her to continue her manipulative ways.
You will probably have to kick her out. Brace yourself for that. Make sure you and your GF stay on the same page because this could really do damage to your relationship.
Regarding her prospects, can she get a GED? School just doesn't work for some people. I was one of them. I HATED school and almost flunked out just because I was so freaking bored. I would have done much better had I dropped out and gotten a GED. I could have finished faster, with a better GPA and not had to deal with all the BS.
You say she's a special case. Unless she has special needs (she's developmentally disabled) then she is not a special case, she just thinks she's one and she's convinced you of it too. She's just a child that grew up without boundaries who has morphed into a teenager who doesn't respect anyone. You won't get her respect by giving in to her demands. She will see that as a sign of weakness and she will only get worse.
Has she been in trouble with the law? If so, I would look into some of the work/learning camps they have for teens. Those seem to really make a difference for the people who go through them.
This has been a bit disjointed because I'm writing as things come to me but hopefully it makes some sense. I hate to tell you but unless something drastic happens to change her, she's probably going to have to hit rock bottom before she decides to change herself. She's not anywhere near that point yet so it could get a lot worse before it gets better. Don't let her take you and your GF with her. You guys are going to need eachother because this is probably going to be a hard journey and you'll need that support.
Good luck to you. I hope things work out as best they can.