In California the answer is possibly if you mean live with your family. But there a major custody issues that need to be addressed. If your girlfriend is being abused she can go to to child protective services for your community.
As well, there are probably papers and custody issues in relationship to the divorce. So most likely the Court would need to be contacted.
You should contact local counsel or legal aid in your community.
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She might be able to live with you, but it's not as simple as just calling the police. First of all, if conditions are as bad as you've described, then it may be necessary to call Child Protective Services to investigate. Second, it may be necessary for your parents/guardians to try to get a guardianship over your girlfriend. (I'm assuming you live with your family.) If they do that, then she could live with you. It helps that her dad will consent. However, if your girlfriend just moves in with you without any court order or CPS action, your parents could be in a lot of trouble, since your girlfriend's mom has a constitutional right to her kids unless and until the court steps in.
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