Do the children of the deceased son inherit alongside the existing son and daughter?

The default rule is that grandchildren, both male and female, are heirs. However, they do not inherit if the deceased's direct son is alive, because he excludes them completely from inheritance. This is unless their father (the deceased son) died after his own father but before receiving his share of the inheritance; in this case, they would receive their father's share. So, here they inherit their father's share, not their grandfather's. If the deceased leaves behind only a son and a daughter, their inheritance is by ta'sib (residuary heirship), with the male receiving the equivalent of two females' shares, as Allah Almighty says: "{Allah instructs you concerning your children: for the male, what is equal to the share of two females.}". Thus, the inheritance is divided into three shares: two shares for the son and one share for the daughter.