How should one deal with the husband's brother's wife who is characterized by jealousy, neglect, and competitiveness, and what is the ruling of Sharia on not feeling joy towards her occasions?

One must think well of Muslims and interpret their words and actions in the best possible light. There is nothing in the woman's speech that suggests malice or incites animosity. What the questioner is experiencing is from the whispers of Satan, who seeks to sow discord among Muslims. One should seek refuge in Allah from Satan, think well of the woman, treat her with kindness, counter Satan's whispers by praying for her well-being, and initiate good conversation with her. Responding to bad with good fosters affection and guards against the evil of Satan.