Margherita Agnelli de Pahlen will not disappear. She will not jump off a bridge like her brother, Edoardo, or accidentally overdose like her son Lapo, or die tragically—and prematurely—like so many other members of her rich and powerful family, who are known as the Kennedys of Italy.

Not only has Margherita refused to disappear, but she is also staging a very public fight for what she claims is her just due: the right to know the full extent of her late father’s huge estate, estimated at between $3 billion and $5 billion. Ironically, this mission has caused her to lose what she says matters most to her: her family.

“Come in,” she says, opening the door of her large and imposing château on the shore of Lake Geneva. The pastoral setting of the property, which horses, swans, and rabbits share with a kiwi farm, seems in direct contrast to the fiery mood of the tall, elegant, strawberry-blonde woman of 52 who lives here. Today she is fighting the flu—she’s “full of aspirin,” she tells me—but then, fighting has become routine for her. Since the 2003 death of her father, Gianni Agnelli, the head of the Fiat car company, who was known as the unofficial king of Italy, Margherita, his only daughter and sole surviving child, has been trying to break down what she claims is a wall of secrecy and manipulation regarding his fortune.

She has invited me to her home to explain that, because she dared to demand a full accounting of her father’s estate, she has become a pariah, one that the men who help manage the businesses of the extended 200-member Agnelli family would like to see go away. Margherita’s mother, the venerable Donna Marella Agnelli, as well as her three children by her first husband, the writer Alain Elkann, no longer speak to her. She says she’s persona non grata at Agnelli family events. She says her soft-spoken second husband, Serge de Pahlen, who worked for 22 years for Fiat, was unceremoniously fired in 2004. (Fiat says it is c...