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 is His Slave and Messenger.
The son who died while his father was alive does not inherit from his father who died after him, as it is impossible to inherit when dead. One of the conditions of inheritance is that the heir must be alive even for one moment after the deceased passes away in order to inherit from the deceased.
Since that son does not inherit because he was dead, then his wife is not entitled to any of the inheritance of her father-in-law because her husband himself is not entitled to any share in the inheritance of his father.
As regards the children of that son, they are in principle among the heirs of their grandfather, but they are excluded from the inheritance if their grandfather has a direct son (i.e. if they have a paternal uncle, whether a full brother of their father or their father's brother from the father’s side) because he is closer to the deceased than them, as he is the son of the deceased while they are the children of the son of the deceased, and justice requires that it is the closest person who succeeds the deceased rather than someone of more distant relation. For more benefit, kindly refer to Fatwa 90126.
However, it is desirable for the heirs to give them something from the entire estate before it is divided, in compliance with the saying of Allaah (which means): {And when [other] relatives and orphans and the needy are present at the [time of] division, then provide for them [something] out of it [i.e. the estate] and speak to them words of appropriate kindness.}[Quran 4:8]
If the deceased did not leave any other heirs than those mentioned in the question, then his inheritance should be divided among his four sons and daughter 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); the male is to receive twice 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]
The children [sons and daughters] of the son as we have mentioned have no share in the inheritance as they are excluded due to the existence of direct sons. Therefore, the inheritance should be divided into 9 shares, each son gets 2 shares and the daughter gets 1 share.
Allaah Knows best.