Is allowing a girl to go out in immodest clothing considered an ongoing sin for her mother, brothers, and husband? And are the husband and brothers considered cuckolds in this case? And do they bear sin for not preventing her? And is it permissible for a girl to wear trousers or adorn herself in front of her husband's brother?

A woman is not obligated to wear a specific type of clothing; rather, she must cover her body with any garment that fulfills the Islamic conditions. If the trousers describe your sister's body, then they are not permissible. A woman must observe hijab in front of her husband's brothers and other non-mahram men. You must enjoin your sister to wear hijab and prevent her from displaying her adornment (tabarruj) to the best of your ability. Whoever is content with his sister going out displaying her adornment is sinful and guilty of dayouthah (lacking protective jealousy). If you forbid the evil and prevent it according to Islamic guidelines, then there is no sin upon you.