How should I act towards my mother and brother who condone mistakes made by my younger sister, and should I intervene in her upbringing, or should I remain obedient to my mother despite the distress that causes me?

Filial piety is among the most emphasized duties, and disobeying one's parents is among the greatest prohibitions, as Allah Almighty says: "And to parents, do good," and His saying: "So do not say to them [even] 'uff' and do not repel them." The Prophet, peace and blessings be upon him, urged filial piety, especially towards the mother, and warned most severely against disobeying parents. Therefore, problems should not arise between you and your mother for any reason. It is your duty to rectify your sisters and your family, and if you exert effort in rectifying your sister and she does not back down, and your mother and her brother support her, then you have fulfilled your duty. You must continue to strive for reconciliation gently and maintain your dutifulness towards your mother.