We get the feeling that Cavendish has asked his brother, Denholme, for favors many times before, if only because when he answers his brother's phone call, Denholme says, "Oh, Satan's gonads, not you" (4.1.101). Old Denny is the one who tricks Cavendish into going to Aurora House. This not only keeps his brother safe, but it keeps other people safe from his brother. Since Denny "sat on the board of a merchant bank for thirty years" (4.1.109), he's pretty adept at tricking people.
It's a little sad, because Denny is clearly the last person Timothy Cavendish has to count on. His wife left him, he never had kids, and all the rest of his family is dead. Even when Denny dies of a stroke, no one calls Cavendish to tell him. At least the Hoggins brothers look out for one another.
There's another reason Denny might have put Cavendish in Aurora House: Cavendish admits that he slept with his brother's wife on one occasion. "Was this trap a cuckold's revenge?" (4.1.22), he wonders. We're never sure if Denny knew about this; it's doubtful he did, since his wife is totally daffy. When Cavendish calls her from Aurora House, she admits that Denny had a stroke and has been floating in the carp pond for weeks. Weeks. And she's just been bumbling around the house ever since. We guess that's one benefit to growing old—you don't understand the magnitude of what's going on around you enough to get upset about it.