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There is no way that Faramir would betray his father for Aragorn. The man freely accepted a mission that was madness and would surely lead to his death! To think he would enter a debate involving Denethor on any side but that of his father is folly. And as has already been pointed out, Denethor had the military under his control to the point that they fought to the death to allow him to kill his son and himself.
The way I see it Denethor would have stepped down. After Pellenor Eomer would be squarely with Aragorn, and it's likely that Imrahil would have been, too. When Aragorn and Gandalf explain to Denethor that they are going to assault the Black Gate Denethor likely dismisses it as foolish, but since with the palantir he sees Sauron's might he likely thinks that Gondor has won the battle but the war is still lost and grants Faramir and anyone who wishes to follow him the right to chase a fool's death. Then when Aragorn, with Gandalf, Faramir, Eomer, Imrahil, and the Ring Bearer come riding back to Gondor victorius Denethor cedes control of the city to public sentiment, which would be to the one who the people think is the rightful King.
My guess is Denethor then goes to live in Ithilien to be near his only remaining son.
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