I agree with Kalimac and lindil, there is no way the relationship between Denethor and Aragorn could have been mended. Denethor was too proud to hand over the rule of Gondor to anyone, regardless of lineage or battlefield prowess. While the general populous may have accepted Aragorn as their king, Denethor, already teetering on insanity, would become even more bitter, perhaps to the point of suicide.
And, all insanity aside, remember that Denethor had plenty of justification to deny Aragorn the crown. Gondor had survived for 975 years under the Ruling Stewards, and no one actually believed the King would one day return--this was at best a fairy tale. Denethor, a loremaster in his own right, knew that the line of Anarion was dead, as Earnur the last king of Gondor had been slain by the Witch-King, and was childless. Furthermore, the line of Isildur was already rejected by the Dunedain of Gondor as having a valid claim to its throne, as Ardevui the Last-King in Fornost made the claim on the death of the childless King Ondoher of Gondor. Gondor's reply to Ardevui's claim was:
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'The Council of Gondor answered: "The crown and royalty of Gondor belongs solely to the heirs of Meneldil, son of Anárion, to whom Isildur relinquished this realm. In Gondor this heritage is reckoned through the sons only; and we have not heard that the law is otherwise in Arnor."
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In the mind of Denethor, who was versed in this history, there was not a man alive who had a valid claim to the throne of Gondor. He would yield to no one.