Is what was done considered a mistake, and how can atonement be made for an oath if the sister enters the house again, knowing the difficulty of fasting and feeding the poor currently? Is this action considered disobedience to parents, and is estrangement from a sister considered a severance of kinship ties? What is your guidance regarding these actions, and is mentioning them considered backbiting?

Wisdom and patience are required when dealing with a younger sister. Actions cannot be judged without knowing the type of mistakes made, but if an oath was broken, expiation is obligatory. As for the disobedience to the mother, its assessment depends on the type of error the sister committed; obedience to parents is in what is good and not in disobedience. The mother must be appeased in a way that pleases Allah. The brother's role is limited to advice, guidance, and reminding if the father is fulfilling his responsibilities. Abandoning and quarreling with the sister is not considered severing ties of kinship if it serves a purpose in reforming her, and it is among the permissible forms of abandonment. Marriage is advised with good selection. There is no harm in mentioning the mother and sister in the question, as seeking fatwa is one of the situations exempted from backbiting.