You are wise to be concerned. Although at this juncture it is a bit late to recover the high school years, I think the living one week here, one week there thing is not the best living arrangement. This gypsy sort of living may have interfered with your daughter's ability to bond to one primary caregiver.
It is possible she feels lost and is actually very anxious about her upcoming adult status. As far as I am concerned, I continued to treat my children as minors even after they turned the magical age of 18 because it was clear they were not yet adults. I acted as if nothing ever happened and continued with curfew's, expectation of homework, etc.
Your daughter will continue to need parenting for many years. I would try and stop the one week here, one week there visitation for now and keep her with you full time so you can get a better handle on her mood and behavior. It is possible your daughter may even have a more serious mental health issue that she is able to hide because of her living arrangements. The teenage years are difficult for all children, but is a prime time to see the emergence of chronic mental health conditions and getting a hold of these issues now before she begins to self medicate or seek out people who may take advantage of her is crucial.
Have you tried calling the school guidance department, or school nurse they may have resources you can try. You could also consider the DSS as a resource.
Not every child has specific goals for college, but your daughter does need to be thinking about how she plans to support herself financially. My rule was full time school or full time work or part time each. For dependancy status it is best if she is enrolled as a fulltime student next fall. That way she can remain on your health insurance. Therapy can become expensive and maintaining your health insurance will be important.
As far as education is concerned, if she does not want to seek a traditional degree, what about a certificate program? What are her interests, it is possible to study in every field from art, to forestry to marine biology. Seriously, there is something for every interest. At this point it will be important simple to get her engaged.
In regards to therapy, I would recommend a female therapist if possible and one who specializes in teens and young adults, specifically, young women.
I wish I could give you a more specific answer, I know how hard it is. All I can say is persevere, hang in there even if your daughter resists. She really is just a baby even if she doesn't know it and no one will ever love her like you love her. You are her best advocate.