Is it permissible for a wife to seek a divorce after 12 years of marriage and having 5 children, given that her husband has emotionally and physically distanced himself from her due to his admiration for his brother's wife, even though he does not fall short in financial support, and the wife is still attached to him?

Ibn al-A'rabi says in his interpretation of "the lion is death," meaning that encountering it entails death, and the meaning is to beware of it as you beware of death. Al-Nawawi clarifies that the intention is that the private meeting of a husband's close male relative is expected to cause a greater temptation, due to his ability to approach the woman without objection, unlike a stranger.

Your sister must frankly tell her husband about the obligation to observe the limits of Sharia with his brother's wife and other non-mahram women. Seclusion (khalwa), familiarity, or unlawful looking are not permissible. Furthermore, brothers living in the same house with shared facilities is not permissible; each family must have an independent dwelling. She must also treat her husband well, obey him in what is good, and cooperate with him in obedience to Allah.