What is the ruling on taking one's sister to the market and shops while she is wearing a decorated abaya, given the fear of stirring up family problems if one refuses?

If your sister adorns herself with makeup (tabarruj) or perfume when she goes out to the market, it is not permissible for you to go out with her, as this constitutes aiding in sin. You should explain to your mother the reason for your refusal so that she may advise and guide her. As for verbally reproving her, if you fear that she might fall into a greater sin, such as abandoning the religion, then do not reprove her. Your parents should look into her condition, as she is in need of upbringing and instilling love for the religion in her heart. Cooperate with your mother in reforming her, and avoid advising her if you fear a greater harm. Be careful not to be extremist, as some abayas have slight adornment that is overlooked due to its widespread nature, unlike tight abayas and excessive adornment.