What is the Shariah ruling on a wife seeking divorce from her husband, who is going through a transitional period after his father's death, on the grounds that he does not spend time with her, curses her, and threatens her?

If you have fulfilled your duties towards your wife, such as providing for her and treating her kindly, then she has no right to object to your care for your mother. Her insulting you because of this is an act of disobedience that warrants discipline. Her request for divorce at that point is impermissible. You are permitted to refuse to divorce her until she relinquishes some of her rights. It would have been more appropriate for your wife to help you in honoring your mother. Remind her of Allah and the Last Day, and strive to combine honoring your mother with treating your wife kindly.