Hi, I'd like to help you with your question.
It is obvious that the situation you described could be potentially dangerous. As a provider, I would also be concerned with the safety of the child in the situation. Please continue to encourage the mother to get help. Maybe provide her with a list of shelters and contacts so she has an immediate place to go to if the situation at home gets worse. She needs to understand that she is putting her child's life in danger as well, and sometimes that may motivate a parent to seek help.
I believe you need to contact the police and ask what you can do to file a report and what the police feel are your options. You may also want to consider reporting the situation to the child protective authorities. The child may not be directly threatened, but the situation could become out of control and the child harmed. The local child protective services should be able to give you some guidance on how to handle this.
Also, document any contact you have with either parent and anything that you see with the child. This will not only serve to help you document a history of incidences, but also protect you in case the situation becomes more involved. You do not want to be trying to recall conversations and details if the police become involved.
I hope for the best in this situation, for everyone.