also Why not try your local social services , my be they could pay a visit if you arrange to be they when they arrive , turning it around so your saying to your father that you understand the stress his under looking after your mother .
its not far on both of them , for your father mental heath or your mothers , it would do them both good if your mother was put in to emergency respite , so your father can clear his mind .
your father has open up to you admitting his has hit your mother , so that could be a cry for help from your father , while your mother is in emergency respite , you can talk to your brothers and come to a plan in how you can help your father in taking the stresses away from him in how to look after your mother when she gets home .
social services can put a care plan in place .Its how you word it all to your father with out the whole situation getting out of control , and then your mother changing her mind and siding with your father when getting confused , intimidated from outside help, that’s where SW can give you advice in how to handle it all , I know that social services will put your mother in emergency respite if they feel they is a risk of abuse to a person . it’s a hard situation your in and I sure at the end of the day it is the stresses even if wrong that his hitting your mother , as they both must love each other , if only your father could see reasoning about emergency respite for your mother and put all the care plains in place , thinks could be so good in the future of your mother care at home with him
Good luck