While sea gulls make extravagant passes against a pink-and-blue sky over Martha's Vineyard, Carly Simon lopes across the dockside stage like some kind of flamingo—loose limbed, open throated and lustily singing. An overcoat flaps behind her in the cold breeze, but Simon, at 42, amazingly looks and sounds as hot as she did when she tantalized the country with You're So Vain 15 years ago. "I'm about the happiest I've ever been in my life," she says afterward.

That news is not quite as surprising as hearing Mick Jagger sing Misty, but it's close. To quote from the latest entry in her autobiographical songbook, the storm-tossed pop laureate of her generation is Coming Around Again. The title song from the album is her first hit single in seven years, marking a soaring comeback after several years of commercial failures and absence from public view. "People seem to think I moved to Borneo," she jokes. "That's where you go when you haven't had a hit for a while." Her Vineyard concert—which premiered recently on Home Box Office—marks her triumph over crippling stage fright that caused her to collapse in 1981 during her last public performance. And—best of all—six years after her divorce from James Taylor, she now hasn't got time for the pain. "I remember the soft feelings about James, especially when I look at our children," says Simon, who, as a single parent, is raising 13-year-old Sally and 10-year-old Ben in her now-permanent Vineyard home.

Simon's new strength has been hard won. Incapacitated by panic attacks onstage since she was a child ("I was such a terrible stutterer that my older sister gave me nonspeaking parts in family plays"), she was persuaded by record company executives to make a rare concert tour in 1981. Offstage, her life was being shredded. "James and I were splitting up, Ben had just had a malfunctioning kidney removed in a very serious operation, and I'd lost 25 lbs. because of stress," she recalls. One night in Pittsburgh, panic hit. "I fell to pieces onstage in front of everybody. I became so anxious that I started having heart palpitations." After the first song, she decided to take the audience into her confidence. "I said, 'You can see I'm in trouble up here,' and they said, 'Stay with it.' When it didn't get any better after another song, I suggested that I might feel better if some of them came onstage with me. Fifty people came up, massaging my arms and legs and saying, 'We love you.' " The outpouring was enough to get her through the first show, but before the second one started, she collapsed backstage. Says her sister Lucy, 44, who was with her that night: "I told Carly, 'There's no reason to have to put yourself through that ordeal ever again.' "

Returning to her home in New York City, Carly checked herself into a hospital, where she spent a week under treatment for exhaustion. "They'd feed me intravenously, and then I'd go home at night to feed the kids," says Simon, whose son was still recuperating from his kidney surgery. "Everyone breaks down in different ways—you could call what I had a breakdown or a fall-apart. I was emotionally wrecked and physically exhausted. What held me together was family, friends and my faith that it was going to be all right."

With the help of a therapist and friends like her former New York neighbor John Travolta, who flew from California to be with her when Ben had his surgery, Simon recovered from this dark phase over the next few months. But the thought of ever singing again in public brought back memories of the 1981 disaster in Pittsburgh. Even at the HBO concert, taped in June and designed to make her feel comfortable, with an audience of friends and townspeople, she was more apprehensive than she looked. "I went through about 25 different emotions, from feeling great to being seized up with fear," says Carly, who focused on the live, immediate audience, not the TV cameras. "The paradox of it all is I absolutely love to perform."

She must have been boosted by the resurgence in her career. Although she has outlasted most other pop phenomenons of the 70s, making 14 albums and an impressive number of hits over the past 16 years, her sophisticated style was pushed aside by little-girl singers, such as Madonna. When Carly's hyped 1985 album, Spoiled Girl, "just bombed," as she honestly puts it, "the people at my record company didn't return my calls. I was a reject from every point of view." She came back to the top after director Mike Nichols asked her to write her first film score—for Heartburn, the Meryl Streep/Jack Nicholson film based on Nora Ephron's roman a clef about a disintegrating marriage.

It's a subject Carly understands. Once media darlings, Manhattan siren and Southern balladeer, Simon and Taylor fell apart for many reasons, from male-female competition ("I was secretly hoping I wouldn't have too much success," she says) to Taylor's dependencies on heroin and alcohol. "I couldn't cope with his disease," says Simon. "I couldn't rescue him." Since their divorce in 1981 after nine years of marriage, Taylor, 39, has recovered and remarried. "He's a wonderful father who spends as much time with the children as he can," says Simon. But the next time, she adds, "I'd like to find a relationship that's more balanced."

As she acknowledges, Carly has been on a lifelong "quest for love." She once believed she was "the ugly duckling" among the three daughters of Simon & Schuster co-founder Richard Simon. (Lucy is a singer-composer, and Joanna is an opera singer and new cultural correspondent for TV's Mac-Neil-Lehrer NewsHour.) "My mother used to show me how to do little dances to get my father's attention," says Carly. Boy-crazy as a teenager ("I'm too tall and sprawling to flirt"), she took her first lover at 16, living with a future novelist, Nick Delbanco, during summers on the Vineyard.

Since her breakup with Taylor, she has dated an interesting array of men, from New York Mets first baseman Keith Hernandez ("He's unperturbed by his masculinity") to former Dynasty actor Al Corley ("He was kind to the kids"). Two years ago she impulsively announced her engagement to Russell Kunkel, her ex-husband's ex-drummer. "Russell's a true gentleman who idealistically thought, 'Why can't we all be friends?' " Carly says. "We were doomed from the start." She's stopped seeing actor Albert Finney ("He makes you feel appreciated, even if you're one woman among many") after a short-term romance. Carly is just beginning a relationship that could turn out to be serious. "He's a fascinating, attractive man, a black-Irish poet with an imagination like James Joyce," she says of her friend (whose name she won't disclose).

It's a typically perfect summer day at the Vineyard. Simon is leaving her pink-and-beige-trimmed, two-story fantasy version of a shingled beach house, driving past the sheep grazing on her 35 acres to pick up her children at a movie theater in town. "By now I'm basically the chauffeur," she laughs. "But bedtime—when I read to the kids and we make up stories—is still sacred." A devoted mother, Carly is unusually sensitive to childhood pain. "She feels their ups and downs," notes her sister Lucy. This afternoon Carly is immediately aware that Ben is feeling down because none of his friends are around. "How about going out to dinner with your mother?" she asks. Warming to her attention, Ben—a shy comedian and the spitting image of his father—protests, "Mom, are you going to do one of your Monty Python silly walks? You'll make me feel like I'm being embarrassed under a magnifying glass." Observes Sally, a young beauty who has her mother's broad mouth and lips: "Some mothers don't give their kids a chance, but Mom listens."

As always, Carly Simon is listening to her heart and writing songs about it. It's no wonder that her new pieces are all about combining romantic passion with plain old domestic tranquillity. "When I married James, I thought marriage was the end, with no problems after that," she says softly. "I know a lot more about commitment than I did before. I'd very much like to get married again, and I hope that someone will want what I have to give."