You have already given me a lot to think about. Rebecca has expressed some of my concerns very well...
TBH Right now my home is pretty chaotic during school time. I am hoping my toddler will mature some over the summer (he will be two in July). But as long as the chaos continues, the environment might not even be the best for a hyperactive child.
The family has a painful history (Mom is deceased, I don't think they know where Daddy is...) There are definitely emotional issues and probably organic issues. The girl's little brother is dx'd ADHD and on meds. Auntie is not lenient on discipline, but I think she often just doesn't know what to do with these beautiful, yet rambunctious children. I believe she would support any rules I impose.
I think Auntie would be okay. I am more worried about how the child would take it if things did not work out. I wouldn't want her to think I gave up on her, etc., Basically I don't want to get into it unless I am willing to take whatever comes and keep at it for the long haul.
Laws in my state are very lenient. We would probably have Auntie withdraw her from school and file the "intent to homeschool" forms. Beyond that the state will hardly care.