What is the Shar'i ruling on a wife who neglects her home and children, is extravagant in spending, and lives with her husband in his parents' home without bearing the burdens of living expenses? And how can one deal with such situations that cause distress and family problems?

It is the wife's right to have independent and suitable housing, and she is not obliged to live with her husband's family or serve them, even if doing so is an act of kindness. If the brother's wife is negligent in managing her household affairs, she should be advised gently. If that does not work, then relatives whose words she accepts can speak to her, while being careful to avoid anything that might cause animosity.