When Robert and Jeanette Schwagerl purchased the house on Quail Hill in Amagansett in 1989, it had been for the most part abandoned. “I was going to tear it down,” Mr. Schwagerl said during a recent tour. Within a year, he had designed a new house and hired Ed Hollander, a landscape architect, to plan the grounds. But the Schwagerls soon fell in love with the existing house and abandoned the idea of demolishing it. Over the years they made a few cosmetic changes, but by 2010, with two teenaged children. Mr.