Praise be to Allah.
The scholars differed as to whether the woman in iddah following her husbands death has to stay in her house. There are two views, the more famous and stronger of which is that she has to stay in the marital home. This is the view of the majority of scholars, including the four imaams.
They used as their evidence for this ruling the Sunnah as narrated in the Hadeeth of Fareeah bint Maalik (may Allaah be pleased with her) who said that she came to the Prophet (peace and blessings of Allaah be upon him) and asked him whether she could go back to her family of Banu Khudrah. Her husband had set out in pursuit of some slaves of his who had run away, and when he caught up with them at the edge of al-Qadoom they had killed him. She asked the Messenger of Allaah (peace and blessings of Allaah be upon him) to let her go back to her family because her husband had not left her in a house that he owned. She narrated: The Messenger of Allaah (peace and blessings of Allaah be upon him) said Yes, so I walked away until I was by the apartment, or in the mosque, then he called me or commanded me and I came back. I told him the story again about what had happened to my husband, and he said, Stay in your house until the appointed time [i.e., until your iddah is over]. She said: So I spent my iddah there, four months and ten days. When Uthmaan was the khaleefah, he sent word to me and asked me about that, so I told him and he followed it and ruled in accordance with it.
It was narrated by Abu Dawood, al-Nisaai, al-Tirmidhi and Ibn Maajah, and classed as saheeh by al-Tirmidhi, Ibn Hibbaan, al-Haakim, al-Dhahabi, Ibn al-Qayyim and others.
Ibn al-Qayyim (may Allaah have mercy on him) said:
There is no reason to reject this clear saheeh Sunnah which Uthmaan ibn Affaan and other great Sahaabah accepted. (Zaad al-Zaaad, 5/691)
A woman who is in iddah could be faced with an emergency such as the fear of the house collapsing, a flood or an enemy, or she could feel lonely, or she may be living among immoral people, or the heirs may want to make her leave the house, or by staying she may lose her children or wealth etc. In such cases it is permissible for her to move wherever she wishes, and she does not have to move to the nearest place. This is the view of the majority of scholars among the Hanafis, Hanbalis and Maalikis.
This is on the condition that she can still adhere to the rulings of iddah in the new home as she did in the previous home.
If a woman is able to manage her affairs from the marital home, she has no reason to move. For example, she can delegate a trustworthy person to follow up the inheritance or property. If your mother is able to do her iddah in the house in which she was living with her husband when he died, then she should stay there. And Allaah knows best.