What is the ruling of Islamic law regarding a sister who causes division among her siblings and harms them through backbiting and slander, and a brother who believes her and harms his sister, knowing that this sister performs acts of worship such as prayers and supererogatory acts?

What the sister is doing by causing discord between the questioner and her siblings is backbiting (namima) and a major sin (kabira). Nevertheless, we advise the questioner to pardon, forgive, and overlook their harm, for they are her siblings and have rights of kinship. Forgiveness and patience are among the highest virtues and are matters of resolve that Allah and His Messenger have commanded, and they increase a servant in honor. True strength lies in curbing one's self during anger. As for the distress the questioner feels in her chest, it is an inner thought (hadith nafs) that is forgiven. She should thank Allah for His blessings and make part of her gratitude the forgiveness of her siblings, maintaining ties with them, and being patient with them, while also having the option to limit the relationship if she fears their harm.