Bismihi ta'ala
I think the initial response you would probably hear is be patient, he is probably under pressure, try not to take sides, and so on.
However, if such a man has no consideration for religious teachings or moral conduct, then the only solution is authority. Once upon a time elders would intervene, and such a husband/father would be deterred and feel ashamed, resulting in stopping such behaviour. Unfortunately, our communities do not have that level of respect anymore.
It starts with your mother, as she needs to have the courage and ability to leave him. She must know that by her staying in this relationship she is exposing her children to violence, trauma and irreversible damage. She probably comes from a mindset that no matter what, the husband/father can do anything, but this is extremely wrong and damaging.
By contacting the authorities, although your mother, or even some family members would be upset with you, but you are stopping and preventing harm upon your mother and your siblings.
The police, social workers, court, etc will be able to give something to him that you or your mother cannot, and that is help. He needs help, for anger management, maybe for mental stability. Maybe just a reminder that he cannot get away with this kind of oppressive behaviour, and so on.
You will certainly be doing the right thing and bring this to an end.
These are my views on domestic violence and living with someone who systematically and continuously abuses family members. Of course, you should try to consult with someone close to you, and reach out for help, and also pray for your father as well.
In shaa Allah other specialists in this forum will give suggestions and advice to you as well.
With prayers for your success.
