What is the ruling of Islamic law regarding the younger sister remaining in her brother-in-law's house? And do I lose my guardianship over her, given that I am disabled, despite my financial capability? And what is the ruling regarding my brothers refusing for her to live with me?

Custody (حضَانة) is a religious obligation. It is a collective obligation (واجب كفاية) if there are multiple custodians, and an individual obligation (واجب عين) if there is only one.

Scholars differ on the age at which custody for a girl ends: Hanafi school: The custody of a girl ends when she reaches the age of desire (nine years old), and she is then placed with her father. Maliki school: The custody of a girl continues until her marriage and consummation. Shafi'i school: Custody continues until the age of discernment (تمييز), then the girl is given the choice between her father and mother. Hanbali school (preferred view): The girl must be with her father from the age of seven until puberty and marriage.

What is agreed upon is the protection of the child from corruption and the consideration of their best interest. If a girl reaches the age of thirteen, she has reached the age at which her custody ceases according to the majority of scholars.

If her father is elderly and semi-ill, then the one who protects and guards her from corruption is more deserving of her. If one of her brothers is fit for this task, then he is more deserving of her. If there is no one among them who possesses these qualities, then the most competent of her relatives should take her.

A girl should not be with her brother-in-law unless he is a mahram to her, except in cases of necessity. The right of a disabled brother to protect the girl is not forfeited unless he is unable to safeguard and protect her.