Is my father obligated to relinquish his share of my grandmother's inheritance to my deceased uncle's children, knowing that my grandmother had verbally renounced her share from her son to them, but then passed away, and the city apparatus refused to validate her signature and is requesting a renunciation from her legal heirs?

If the sane grandmother waives her share of the inheritance in favor of her grandchildren, her waiver is valid and considered a gift (hibah (definition)). A gift becomes binding upon possession. So, if the grandchildren take possession of the grandmother's share, the gift is complete and binding, and the grandmother has no right to revoke it, nor do your father and uncle have the right to claim this share after her death. However, if possession of the share, or a part of it, has not been taken, the grandmother has the right to revoke it, and if she dies, the gift becomes void regarding what has not been taken possession of. Based on this, the bank balance and the car, which have been taken possession of, have become the complete property of the grandchildren. As for the land, it follows the ruling of possession; if it is in their possession, then the gift has become binding.