As a result of the above I am not big on home-schooling either though in some cases it seems necessary....
I went to a normal preschool, a normal primary school and a normal secondary school and my social skills are pretty bad. I was bullied for most of the time I was in school. I do not have any friends other than my husband, whom I met online... Anyway, it doesn't seem all that relevant to this thread to argue about whether homeschooling is better or worse for social skills than school, so let's leave it at that. If you want me to ramble on about homeschooling vs school-schooling, just let me know.
I don't think it's a good choice for her either, but if you're supportive of her and help her explore the topic by letting her read more about it and talk to people doing that actual job she's likely to find that out for herself, rather than just being told by you.
Who knows what your father would've said if asked about wanting you to become a physician? He might have said that all he was doing was trying to give you the tools to succeed as well.
I'm all for providing guidance to kids and young adults, but if someone doesn't want to learn something it's virtually impossible to teach them. Show them why it's important they learn something... let her make a few mistakes. When she graduates from highschool it'll very quickly become blatantly obvious that getting a job that pays decently isn't that easy without a degree. After a year or two she'll probably either have learned to be satisfied with a low income, have found one of the few higher-paying jobs that don't require a degree or have decided to go to college and work at it. It's not a disaster if she doesn't go to college at age 18, really. 20 (or 30 for that matter) is still plenty young.
Only if it comes from within... and only if it concerns something that you think is worth doing. The moment I don't believe something is worth doing all my discipline vanishes. When I started college I thought it was worth doing it... I'm not sure anymore hence I dropped out.
It doesn't sound like a big request, BUT she didn't choose to be in school... the state decided that for her. The state is deciding for her that it's important for her to learn about trigonometry, Hamlet, etc... If I were to decide for you what I think is important for you to learn, would you just take my word for it and read it once? Would that be reasonable? What if it wasn't me that did that, but the state... the state requiring you to read one book (assigned by them) a week... Would just take 5 hours a week. Perfectly reasonable, right?
Anyway, if your request is so reasonable, then surely you could explain to her why it's reasonable...
Fact is, all around her she sees adults that don't remember anything they learned in highschool, but that expect her to learn it anyway, while she feels there's more important things to learn at the moment, such as social skills, which she's teaching herself by hanging out with her friends. Who knows, that might exhaust her enough to not care about reading her assignments. And who knows, she might be right... it might be more important to her future than reading her textbooks once.
Look... I'm not trying to bash you. I bet you're a good parent overall, you seem to want the best for your daughter. But really, so does she, and just because you're older doesn't necessarily mean you know better. Teenagers are often hard to talk to mainly because their parents still think they know things better whereas the teenager knows that the parent doesn't know everything.
My father-in-law said something to me recently that was pretty much on topic. When my husband was 15 or so and not doing things exactly the way my fil wanted him to, my fil's friend told my fil "Look, you've been saying since he was born that you want him to grow up and be independent... now he's doing exactly what you wanted him to.". My fil had to agree with him on that point.
Independence means that you make your own choices, and some of those choiced might not be the ones that your parents would want you to make. And 18yo is not the point in life where you should go from no independence to independence... Independence is something that should grow and grow before that point.
Ugh... I'm not sure how to get this across clearly... I'm feeling I could've phrased this better but I just don't know how. Sorry.
Perhaps you should try talking to parents whose kids are in their late twenties or older and see how much they worried about all kinds of things and how their kids turned out fine. Just a thought. 
All I can advise is: pay attention to your daughter's interests, to the things she does well and the environments in which she thrives, and be open to all career possibilities. Maybe your daughter has a learning disability which has not yet been diagnosed, maybe she could be helped by tutoring, but maybe she is (like me and like many other people) very bright without being well suited to academic life. I hope you and she continue to seek guidance for her to make the most of her unique gifts. 
) Also, if she goes to the shelter after school, she may simply be too tired or stressed from the rest of her day. You really would have to ask her what is going on. Best wishes...
Sensory- and people-wise I know this would be a disaster though.