Is it permissible for my mother to take her share of her parents' inheritance if the estate was divided according to the obligatory bequest (al-wasiyyah al-wajiba), which stipulates that the share of a son who died before his parents be set aside and distributed to his sons and daughters?

Since the grandmother died before her parents, she has no share in their inheritance. This is because the condition of their being an heir alive at the time of the inheritor's death was not met. Consequently, her children have no right to inherit from their grandfather and grandmother. Your mother is not entitled to take anything from the estate. What is called the law of obligatory bequest (al-wasiyya al-wajiba) is null and void, and no scholar has ever endorsed it.