Once again, Color Andy proves to be someone other than who we thought he was. B&W Andy once helped Floyd maintain an illusion for a correspondence-club ladyfriend. He helped Otis maintain an illusion ("It's falsifying!") for relatives who thought he was a deputy. Color Andy helped Goober maintain an illusion of having a gas-station empire. But in this episode, he seems hell-bent to expose cousin Bradford's "falsifying," and frankly, to have some underlying grudge against the guy. Why? Because Bradford lied via mail? Just like Floyd and Otis? And with Otis, Andy made a point of wanting to help: "You never know how these things might turn out right!" Andy's getting righteous and losing empathy kind of late in the game.
This is the only episode I can think of in which Andy uses the coercive authority of the Sheriff's office to satisfy a personal desire. Note that he's in uniform and has Bradford in the courthouse when he tells him --with no hint of "merely suggesting"-- to be out of town within a few days. Yet what could Andy do if Bradford DIDN'T leave? Kill him? As far as I can see, Brad broke no law in Mayberry, so Andy couldn't arrest him. So beyond scowling and bluffing, the only logical next step would be illegal personal violence.
Is Andy incensed because Bradford has lied to Delicate Aunt Bea?? She hadn't seen Bradford in decades, and probably wouldn't again for decades to come (i.e., at their age, never), so what would it hurt to maintain the illusion? Note also that it's Andy who breaks the truth to Bea and thus causes whatever disillusionment she experienced. B&W Andy would have given Bradford a lecture and let him find his own way out of town, like he did with "David Browne," or bluffed him into leaving like he did with "Roger Hanover," but at any cost would have let Bea keep her happy image of the rich relative. The logical conclusion I draw from the fact that he didn't is that Color Andy has found someone for whom he has more hatred than he has compassion for Bea.
There is an ironic redemption to the episode, when, as Bradford leaves town, Clara excitedly tells the folks gathered at the Taylor house to see Bradford that he has been called away for a special mission for the U.S. State Department. For the assembled guests, she lends the credibility of someone who had always been skeptical about Bradford, and she demonstrates that she has *finally* accepted the idea that Bea could have at least one relative as important as Clara claims all her dead kinfolks were.