Long before the Taylor Swifts, Miranda Lamberts and Brandi Carliles, Carlene Carter set the standard for today’s independent, self-empowered, and irrepressible female country artists—and she did so when country music, as Barbara Mandrell sang in her 1981 Country Music Association Single of the Year, “wasn’t cool.” Three years earlier, the daughter of 1950s and ’60s country crooner/honky-tonker Carl Smith and the Carter Family’s June Carter Cash — and stepdaughter of Johnny Cash — released her self-titled debut album, on Warner Bros. The label had sagely sent her off to London with the idea of recording country music with a rock band. But it wasn’t just any rock band: Carlene Carter was recorded with New Wave singer-songwriter Graham Parker’s cutting-edge The Rumour, and produced by its key...