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.
Concerning the house which the son gifted to his mother, if he gifted it to her at any time before his final illness, and his mother took possession of it before he died, and she had control of it as its owner in such a way that she could sell it or rent it out and the like, then this house's ownership was transferred to the mother by it being gifted to her, and it is no longer the son's property. If the mother dies, the house would be the property of her heirs and the son's wife has no right to claim this house since it is not part of her husband's inheritance.
However, if the gift was not concluded, such as if the son died before the mother took possession of the house, then the house is part of his inheritance and his wife has a right to it, whether before or after the death of his mother. Hence, the wife is entitled to a share of the house in proportion to her legitimate share in the inheritance.
Similarly, if the son gifted the house to his mother during his final illness and his mother took possession of it, then a gift which is given during the final illness is effectively a bequest, and a bequest to the mother is not valid because she is an heir. In this case, the son's wife has the right to claim her share of the house. In case of dispute, it will be necessary that all parts present the case to an Islamic court, if there is one, or verbally ask scholars who may act as judges.
If the deceased woman did not leave any heirs besides those mentioned in the question, then her two daughters get two-thirds as their legal share as it has been confirmed that the Prophet, sallallaahu ‘alayhi wa sallam, gave a share of two-thirds to the two daughters of Sa‘d ibn Ar-Rabee‘. [Ahmad, Abu Daawood and At-Tirmithi]
Ibn Al-Munthir said: “The scholars unanimously agreed that two daughters have a right to two-thirds of the inheritance (as their legal share).”
The remainder should be divided among the son's son and the son's daughters by Ta‘seeb (by virtue of having a paternal relation with the deceased and not having an allotted share, so they get what is left after the allotted shares have been distributed), with the male having a right of two times the share of the female as Allaah says (what means): {Allaah instructs you concerning your children [i.e. their portions of inheritance]: for the male, what is equal to the share of two females.}[Quran 4:11]
Therefore, the inheritance should be divided into 12 shares. The two daughters get two-thirds, which is eight shares, and each gets four shares; the grandson gets two shares; and each granddaughter gets one share.
Allaah Knows best.