Re: "I found some people's advice helpful, and for that I'm grateful"

You're in a really difficult situation, and the main gist that I believe many responses were trying to present is that this kid needs immediate help and that the help must be initiated by her biological parents.  The father of this child has no business foisting responsibility for this child's welfare (other than what could be considered reasonable) upon you - his daughter is HIS responsibility.

Now, if the mother is causing problems, it may be necessary to change custody/visitation arrangements so that the child will be in a structured environment.  Having survived a child with borderline personality disorder and another diagnosed ADD, it is not only "trying" on the biological parent, but an absolute nightmare for a stepparent.  The father of this child should, strictly for the child's well-being, intervene, ASAP, even if the mother is reluctant to assist!  You should not be held responsible for seeing that this child gets the help that she needs.

Now, if I were in your shoes, I would not budge on this issue - either get help for this kid, or I don't want her in my home.  Sounds drastic?  Yepper.  Sounds mean?  Perhaps.  But, from my own experience, a child with these sorts of issues is not only a danger to herself, but to others, as well.  Again, my suggestion is:  get yourself to a counselor, alone, if need be. 

Best of luck to you.