All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
The request that your father made, that your mother stays in his house after his death is considered a will in favor of an heir, which is forbidden in Islamic law and cannot be effective except with the consent of all heirs. Your mother has no right to sell the house or any other property of your father's estate and favor your brother with it. What your father left has become the property of all the heirs, and none of them has the right to dispose of it independently. If all the heirs agreed to delay the division of the estate, then there is no religious impediment to it as long as all of the heirs are sane mature adults and are willing to delay it wholeheartedly. However, if some of the heirs disagree about the delay, then it is impermissible to delay the division of the estate. Rather, it is incumbent to divide the estate among the heirs according to the Islamic inheritance laws. Please refer to fatwas 96556and 106981.
As for the rent to own contract, please refer to fatwa 2884.
Allah knows best.