Do not get any legal entity involved....you will regret it. The only exception is in cases of physical or sexual abuse.
Years ago, I was laid off from my job and had to relocate to look for another one, which I got within 6 months. My sister offered to let my daughter , who was 13 or 14 and beginning to be a real probelm, stay with her out of state and start the school year. Before I knew it, my sister sent me papers to sign giving her legal guardianship on the basis that I was an unfit parent (the year before I became clincally depressed , but got fine with theray and antidepressants). I refused to sign but my daughter ended up staying the entire school year and was more angry with me than ever when she did come home. A lot of therapy went on for her for the next couple of years.
To some extent, I felt a lot of guilt for ever letting her go to my sister's in the first place, untill years later, when our Dad died. My sister wanted to immediately put our Mom in a bad nursing home near where she lives, while I wanted to put her in a good one that specialized in Alzheimer's patients near where I lived. We fought, probably because it was the first time I really stood up to my sister. Our Mom got freaked out by the idea of any nursing home, so I left with my Mom and a few of her possessions and brought her home to live with me until her death a few months later. During this time, my sister tried to get legal guardianship of Mom based on my "instability". She was not successful. Apparently nobody but her thiinks I am unstable to the extent that the legal system had to get involved - on either occasion. I do not speak to my sister and have no plans to ever do so....so keep this in mind before you go to extremes with your own sister. Her life turned out differently than yours did, but you haven't walked in her shoes, and a lot of teenagers rebel and make mistakes before they straighten out - and they live in himes just like yours too.