Will the elder brother be questioned if he is unable to prevent his sister from engaging in reprehensible acts, not wearing the hijab, and working in mixed environments? Is his fear of family problems a valid justification for not using strictness with her? What should he do regarding her?

We recommend supplicating for their guidance, as a righteous supplication may be a cause for their guidance, and "the one who points to good is like the one who does it." You have done well by advising your brother and sister, so continue and do not despair, and let gentleness and kindness be your guide. A brother has guardianship over his sister in the absence of the father, whereby he must prevent her from causes of corruption. However, this is not like the father's guardianship, so you must object to her as much as you are able. What you are unable to do is waived from you. You should be gentle and wise in dealing with your mother and sister, and strive to nurture faith, and hold Quranic circles and educational sessions at home.