What is my duty towards my sisters and mother, especially since I see that their actions (such as wearing tight clothes, putting on makeup, my eldest sister's adornment and her joking with non-mahram men, and my mother's mixed-gender work environment) contradict Islamic law, even though they are committed to prayers and good morals?

You must initiate sincere repentance for violating the sanctity of Allah and for listening to music excessively. Regarding advising your parents and sisters: Begin with a kind introduction, mentioning their good qualities before offering advice. Advise your mother and sisters with gentleness, kindness, and decorum, reminding them of the hijab and repentance, and that death comes suddenly, citing the noble verse: "Say, 'O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful.' And return [in repentance] to your Lord and submit to Him before the punishment comes upon you; then you will not be helped. And follow the best of what was revealed to you from your Lord before the punishment comes upon you suddenly while you do not perceive." If your mother does not benefit from the advice, leave her be, as she is not like others. It is permissible to shun sisters if shunning will lead to their reform. Increase your supplications for their guidance.

Finally: The hijab is an obligatory duty, and repentance from sins is obligatory. It is not permissible to accept the wrongdoing committed by a sister, even if the mother agrees; for there is no obedience to a created being in disobedience to the Creator. Your maternal cousin is a non-mahram, and you must deal with him as such and avoid anything that leads to temptation.