Check my comments. I can tell you 10000% that the right moves need to be made if OP wants to get this girl help. There are simply not enough places to put abused children... period. The cops/DCS will do their best but you need to provide them with an absolute reason AND resources they don’t have (a home for the child) if you want any kind of predictable/positive outcome.

I had a similar mindset to you.. trust the system, call the authorities, etc. until I started teaching.. getting this girl the safety she deserves will not come without careful thought (documenting, pictures, etc.) and those who care fighting tooth and nail for her.. if simply reported the result may be the mom is warned that she can’t trust her family to keep her dirty secret, a slap on the wrist, mom leaves legally with the child, the outcome for the child is terrible.

I can tell you from experience, DCS/CPS is like the DMV but 100000x underfunded, understaffed, overworked, and under-supported. This is not Law and Order, this is a real child’s real life at stake.