What is the Sharia and rational advice for a husband who wants to marry a second wife, while his first wife refuses and threatens to neglect her marital duties and divorce, and he has reached a point where he wishes her dead, knowing that he does not have the love for her that she desires?

Treat your wife with kindness and explain to her that a man marrying another woman is not an injustice to her. You are not required to inform her of your marriage, but you are required to be just between your wives. Both of you should be keen on speaking good words that bring affection, even if it requires lying. Lying is permissible in three cases, one of which is a man speaking to his wife and a woman speaking to her husband. Feelings of love are not a condition for the stability of married life, as Umar (may Allah be pleased with him) said. In summary: Treat her kindly, do not mistreat her, and fulfill all her rights. If you wish to divorce her, then release her with kindness.