How do I deal with a mother's discrimination between her children and her different treatment of each of them, in addition to a brother's injustice towards his sister and the mother's intervention on his behalf?

It is not permissible for a brother to wrong or harm his sister, nor is it permissible for a mother to assist a tyrannical son against his sister. You must support your wronged sister to the best of your ability. However, it is not permissible to raise one's voice at the mother or harm her in any way. Disrespecting parents is the deliberate harm to them that people commonly recognize as such.