There’s a certain kind of Hamptons house that tries to do everything—and then there are the ones that actually pull it off. In the sleepy Water Mill area, a newly reimagined estate by Los Angeles-based designer Jake Arnold feels less like a weekend home and more like a self-contained boutique resort, where mornings can start in the garden and evenings wind down around a fire pit—all without ever leaving the grounds.
Arnold, who recently collaborated with John Legend and…

