Is the reaction of not weeping over the grandmother's death—despite having grieved over the death of my maternal cousin previously—considered normal, or is there something wrong with it, taking into account that the grandmother died after a long illness which it was hoped would be a purification for her and a preparation for the family?

Crying over the deceased is permissible, not obligatory or recommended. There is no blame on someone who refrains from it, as this does not indicate anything negative. Some scholars view crying as an act of mercy and goodness, based on the actions of the Prophet, peace and blessings be upon him, while others believe refraining from it is preferable. Permissible crying is that which involves tears without sound, whereas crying with sound is called wailing. Prophetic traditions have clarified that crying out of mercy does not contradict acceptance of divine decree; rather, it is a sign of compassion in the hearts. Patience in the face of calamity is obligatory, and an even higher station is for the servant to thank their Lord for it.