This doesn't soundto me like a schooling issue as much as a child protection one. While a child lives in an abusive/neglective environment, learning will be minimal. Precious time is being lost as this is the period when she should be learning rapidly, not to mention how she is suffering emotionally from the neglect.
Hard though this may sound, I think this is a matter for social services to deal with. Why haven't the school called in an outside agency? I honestl think that if they haven't, someone should.
Sorry if this sounds harsh, I know it must be hard if it is a relative, but I would contact social services myself and ask them to get involved and assess the family. Maybe they can offer the help that this family needs, and if not, place the child in a more nurturing environment - if it came to this, you may find that your MIL would decide to try for custody.
Until the chaos of her life is sorted out, she has little hope of developing a love of learning. If you are not fed, you focus on getting fed, if you are cold, you focus on getting warm. If you feel unloved, you focus on finding love. It is not until all these physiological and emotional needs are met that you can focus on learning.
I hope this doesn't sound too harsh - I have worked with many such children and have seen the effects if things are left and problems aren't addressed. Good luck, in whatever you decide to do - your neice is lucky to have you caring about her.