My daughter's biological mother has been arrested quite a few times for having sex without disclosing her HIV status. Her judgment, if she ever had any, is severely compromised by drug use and depression. She is extremely promiscuous, and prostitutes herself for money. She was run out of one city in upstate NY, and moved to NC where she did the same thing all over again.
I washed my hands of her a long time ago, and for me, it had nothing to do with scripture (just being honest here). I just got fed up. I still love her and all (and I thank her for blessing me with the fruit of her womb), but I had to let that chick go. Some folks just don't want to change. Some folks like their mess.
If I were your cousin, I would sit the young lady down, and tell her that I love her and really want to help her out, but I can't help her if she doesn't want to be helped. I would tell her that she desperately needs therapy, and that if she's going to be in my life, she's going to have to do better with hers. Either get in therapy, or find some place to live. Also, if the young lady chooses to stay and get help, I would establish house rules that are clear (in writing) and fully understood. I would advise her that if she breaks one rule (i.e. doesn't clean after herself or stays out too late, etc.), she has to go. No three strikes. One strike. You can't respect my home, you gotsta go.