Can a sister be punished for her brother's sin and his laxity in religion?

If the brother accuses the girls of indecency, explicitly or implicitly, it is slander (qadhf). If he mentions their faults in their absence, it is backbiting (gheebah). If he attributes to them what they did not do, it is calumny (buhtan). His wife shares in the sin by spreading these matters.

Not performing prayers is one of the gravest sins. They must be advised with wisdom and good counsel, and reminded of the seriousness of their actions.

It is not permissible to listen to them. They must be denounced, and their company should be abandoned if they do not desist, based on the words of Allah Almighty: "And He has already revealed to you in the Book that when you hear the verses of Allah being denied and ridiculed, do not sit with them until they enter into another conversation. Indeed, in that case, you would be like them. Indeed, Allah will gather the hypocrites and disbelievers in Hell all together." (An-Nisa: 140).

Allah does not punish a soul for the sin of another, based on His words: "Every soul, for what it has earned, will be [held] in pledge." (Al-Muddaththir: 38) and His words: "And every soul earns not [evil] except against itself, and no bearer of burdens will bear the burden of another." (Al-An'am: 164).

However, one can be held accountable for listening without advising. If you fulfill the duty of advising, you are safe, by the permission of Allah, based on His words: "So when they forgot that by which they had been reminded, We saved those who forbade evil and seized those who wronged with a severe punishment because they were defiantly disobedient." (Al-A'raf: 165).