All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
First of all, we say that you are wrong to describe your mother as a ‘very money obsessed’ and ‘ruthless’ person; so you should fear Allaah and repent to Him. You should know that being kind and dutiful to your parents in your life and keen on their well-being after you die, comes in priority over being keen on the well-being of your wife and your children as the parents come in priority in this regard, especially the mother. Abu Hurayrah narrated that a man came to the Prophet and asked him: “Who deserves my good company more?”, and he [the Prophet] replied: “Your mother.” The man asked: “Then who?” The Prophet said: “Then your mother.” The man asked again: “Then who?” The Prophet again replied: “Then your mother.” The man asked again: “Then who?” Thereupon, the Prophet said: “Then your father.” [Al-Bukhari and Muslim]
Besides, you should not preoccupy yourself with something that has not taken place yet, as it may happen contrarily to what you expect, as the one who is thought to die last may die first or the like. Indeed, the Salaf (righteous predecessors) hated asking about things which have not taken place yet. An-Nawawi talked in Al-Majmoo' about the Companions saying: “Their Fatwa was limited to things that already happened and they objected to being asked questions about what did not take place.”
In any case, if we presume that the matter happens as you expected, then your parents have the right to ask for their share in the house even if this leads to selling it. What you mentioned about your wife and children moving away to another house and your children leaving the school or the friends they used to have; then there is no harm on them in doing so, and this is not an impediment that would prevent your parents from taking their share in the house.
Allaah Knows best.