Is the wife obliged to stay overnight at her mother-in-law's house at her husband's request if he travels, even though her mother-in-law does not need her service, and would the wife fall under the threat of "you have incurred the wrath of Allah and the angels curse you" if she refuses, and should she apologize to her husband for refusing his request?

May Allah reward you for your kindness to your husband's mother and for helping him fulfill his duty to her. This is indeed a sign of noble character and beautiful companionship. Your husband's statement that you deserve Allah's wrath and the angels' curse for not staying overnight with his mother is incorrect; staying overnight with her is not obligatory for you, and you are not required to obey him in that regard. However, it is preferable to obey him if it causes you no harm. If you do not stay overnight, then apologize to him to appease his heart.