Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
We ask Allah to forgive your father and grant His Mercy upon him. As for your question, there is a Hadtith that Furay'ah, daughter of Malik Ibn Sinan came to the Prophet (Sallallahu Alaihi wa Sallam) when her husband was murdered and said: "Should I return to my people, for he did not leave any dwelling house of his own and maintenance for me? She said: The Apostle of Allah (peace be upon him) replied: “Yes”. She said: ‘I came out, and when I was in the apartment or in the mosque, he called for me, or he commanded (someone to call me) and, therefore, I was called”. He said: “What did you say?” So I repeated my story which I had already mentioned about my husband. Thereupon he said: “Stay in your house till the term lapses”. She said: So I spent my waiting period in it (her house) for four months and ten days. When Uthman Ibn Affan became caliph, he sent for me and asked me about that; so I informed him, and he followed it and decided cases accordingly". (Al-Sunan)
The above Hadith proves that the woman whose husband dies should not move from the house where she got the obituary of her husband, as it is clearly mentioned in some narrations of the Hadith. Some narrations also read that she was living in a remote house.
Therefore, your mother is not allowed to move to a new house before completing her Iddah. As for the excuse that she keeps remembering her husband if she lives in the house is not considered in Shariah, this situation will change as time goes it by, Insha Allah.
The other family members may move to the new house but your mother and the one who takes care of her should stay in the old house. However, she may go to the new house during the day but at night she must stay in the old house.
Allah knows best.