Is the paternal grandmother's disposition of the entire plot of land considered valid, and is it deemed solely her property based on her purchase of it from her husband, given that the husband had secretly bequeathed half of it to his son from another wife without her knowledge? And does the questioner's father have the right to sell the entire plot after the paternal uncle's wife relinquished her deceased husband's share, or must the rights be returned to the heirs of the deceased paternal uncles?

This is a complex issue, and the default approach is to refer it to the Sharia courts.

If the husband sold the entire land to his wife, it becomes her private property, and what he wrote in his son's name is not considered; because it is either a revocation of his gift or a disposition of something he does not own.

However, if the husband did not sell the entire land, and his son's heirs claim that the husband gifted the other half to their son: if it was a will, then the will is void and should be divided with the father's inheritance among all his heirs. But if it was a gift that the son owned and possessed during the father's lifetime, then it is a valid gift, and half of the land belongs to the son and should be divided among his heirs.

The strongest assumption is that the husband's sale of the entire land to his wife constitutes a revocation of his gift, which is permissible for a father. Thus, the land belongs to the wife (your father's grandmother) unless the claimant provides evidence to support their claim.