When Nate Berkus and Jeremiah Brent ’s daughter, Poppy, saw her new room in the family’s restored Portuguese farmhouse , she had ideas. She wanted to keep the original rust-red-tiled floors and antique furniture while repainting the armoire a robin’s egg blue. “She thinks that we have terrible taste, and that everything we pick out is ugly,” says Berkus with a laugh. “She likes crusty French Louis XVI style.” As any good dads (and interior designers) would, Brent and Berkus incorporated many of Poppy’s requests—and the room turned out to be one of the best in the house. Good design, after all, is often a conversation across eras and sensibilities. That historical fluency is central to how Berkus works. His own signature—warm neutrals, collected interiors layered with vintage and antique objects that carry a sense of personal history—didn’t emerge from a vacuum. “As a designer, my job is to know the best historical references,” he tells AD PRO.…