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If neither the father nor the LW is willing to parent this child, and the mother is out of the picture, it may be best if she is sent to a boarding school. There are good therapeutic boarding schools that can help her with her life skills and give her some attention.
I don't recommend it for 99.99% of situations, but in this case, it may be the only hope for this kid. A friend from college was sent to Mooseheart after his mother dumped him on his grandmother. He was there from age 7 to age 18. It wasn't the worst thing that could have happened. It wasn't great, but it was a lot better than the nothing he was getting from his family.