Is it permissible for a seventy-year-old mother to travel from Jordan to Saudi Arabia to live with her son, especially since she lives alone in Jordan and her son's wife and daughters are in the same house on the second floor?

We ask Allah to have mercy on your father. As for your mother traveling without a mahram, it is not permissible except out of necessity, and this is the view of the majority of scholars, based on the hadith: "It is not permissible for a woman who believes in Allah and the Last Day to travel a journey of one day except with a mahram." Some scholars, however, permit it when a mahram is unavailable and the company is trustworthy. As for her completing her iddah outside her home and city, it is not permissible unless there is an excuse that necessitates her living alone. If she is harmed by living alone, then it is permissible for her to travel to you to remove this harm. However, it is not permissible if the harm can be removed by her living with your wife and daughters, or by your traveling to her.