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The kid's mother is insane, her father only sees her for dinner 1 night a week, and now he's taken her away from her primary care-giver (nanny). Of course she has issues.
If no one teaches this kid anything, how would she know how to take care of herself? Get her in therapy, then get the hell out. You have no business being a step mother, and if you continue to live there and ignore this child you deserve to go to prison.