How can one deal with a mother who encourages her daughter to engage in unacceptable behaviors and wrongs her son, who tries to advise his sister, which has negatively affected his psyche and future?

You must call your mother, honor her, and associate with her in kindness, even if she wrongs you and harms you. This is because the mother's right is great, and Allah has commanded kind companionship for parents, even if they are polytheists. Ibn Abbas said: "There is no Muslim who has two Muslim parents, to whom he wakes up seeking reward, except that Allah opens for him two gates—meaning: of Paradise. And if he has one, then one. And if he angers one of them, Allah will not be pleased with him until that parent is pleased with him." It was asked: "Even if they wrong him?" He said: "Even if they wrong him."

You must also forbid your sister from evil with wisdom and gentleness, and hasten to marry if you are capable, for it is among the traditions of the messengers and it secures half of one's religion.