What is the ruling on a paternal uncle refusing to relinquish his share of the commercial shop, which he had agreed upon with the father, and rejecting the pre-agagreed exchange, claiming that the value of his share has now increased?

The resolution of disputes falls within the purview of the Sharia (definition) courts or their designated representatives, as they are best equipped to hear all parties, grasp the reality of claims, evidence, and defenses, and render a judgment. A Mufti (definition) hears from only one party, and his understanding of the issue is limited, thus he cannot issue an accurate ruling in such cases. If the uncle acknowledges waiving his right or exchanging, and the sale was concluded with offer and acceptance, and the session ended, then the sale is complete. He cannot cancel the transaction unless your father agrees, based on the Prophet's (peace be upon him) saying: "When two men make a transaction, each of them has the option [to revoke] as long as they have not separated, and they are together, or one of them gives the other the option. If one of them gives the other the option, and they make the transaction on that basis, then the sale becomes binding. And if they separate after they have made the transaction, and neither of them has abandoned the sale, then the sale becomes binding." If the uncle denies the occurrence of the sale, then your father should involve benevolent people to resolve the issue, or raise the matter before the judiciary and present evidence.