In 1993 media mogul Rupert Murdoch called Sweeney and offered her a promotion and the chance to explore her love of launches, writ large: He wanted her to move to Los Angeles and, as chief executive officer of FX Networks, help him start a cable channel. If Sweeney hesitated before accepting, she had good reason. The family was set up in its first real house—“a sweet Dutch Colonial, the kind you dream about”—in White Plains, New York. Her husband, who had just graduated from law school, had lined up a job at a big New York City firm and was studying for the bar.

“Just when you think you have everything organized, God laughs,” she says. “I spent the next couple of days talking to my husband about it . . . and every piece of the refrigerator was covered with pro/con lists.” Ultimately, she says, it was her spouse’s willingness to move to California and take the bar exam in both states—“a wildly unpleasant experience,” she notes—that convinced her the move could work.

“He looked at me and he said, ‘You gave me law school. The next adventure is yours.’ ”

Sweeney's great adventure at Fox saw her launch two cable channels in three years—FX, which featured a mix of sports, news, live TV and reruns, and FXM: Movies from Fox, the industry’s first studio-based movie network. FX established an early foothold on the then-new World Wide Web, encouraging viewer interactivity with the channel. Murdoch “taught me not to be afraid of any idea,” Sweeney says. In 1996, Sweeney’s former boss Laybourne hired her away to Disney/ABC, where she oversaw the launches of Toon Disney (now Disney XD) and SOAPnet and more than quintupled the Disney Channel’s subscriber base. She ascended to her present position in 2004.

The family’s relocation to the West Coast in the early ’90s proved fortunate in ways Sweeney could never have imagined. When her son, Christopher, was two, she began noticing that he had cognitive issues, so she took him to the pediatrician. She returned home with a diagnosis—something called pervasive developmental disorder—and a feeling of helplessness. After the move to Los Angeles, a doctor examined Chris, by then nine, and told Sweeney and her husband that their child was autistic. “It was, in an odd way, a relief: At least we knew there was something we could read about,” she says, adding that they found “a brilliant speech therapist who willed him to talk. Then we kept throwing a lot of therapy at him.” A seismic change in her son’s development came when Miller decided to go part time. “To have Dad on the ground when Chris got home? It was life changing for us,” says Sweeney. “It was an enormous sacrifice on my husband’s part, but he made it for our family.”

While working for Murdoch, Sweeney met Peter Roth, then president of Fox, whose daughter is autistic. They became “friends and support systems for each other,” says Roth, who now runs Warner Bros. Every year, he says, Sweeney arranges a VIP trip to Disneyland for his daughter, who is passionate about the amusement park. For that, he says, “I will always be grateful to her.”

Sweeney’s daughter, Rosemary, 22, is getting her master’s degree—in, yes, education—at Stanford. Chris, 27, lives in a group home and often comes to visit his parents on the weekend. Sweeney’s face lights up when she talks about her son; it’s clear that she truly appreciates the man he has become. “He calls everyone every day,” she says. “He checks in with his aunts, his cousins, his sister. To me, he is who we would all like to be: that person who never stops caring about everyone in his family and community.”