When Joseph Stalin's only daughter, Svetlana Alliluyeva, packed up her American-born child, Olga Peters, 13, and fled the Soviet Union two weeks ago, it was the latest episode in a tale of peripatetic torment. At 60, Svetlana is a three-time divorcée who has had problems with drinking and depression. She is estranged from two of her three children and alienated from her homeland as well. She is also haunted by the specter of her mother's suicide and her father's tyranny.

Searching for a solution to her personal problems, Svetlana has journeyed restlessly between the Soviet Union and the U.S., apparently unable to decide where her home or loyalties truly lie. She first defected to the West in 1967, after denouncing the Soviet system as "profoundly corrupt." In 1984 she returned to Russia, declaring that she had not been free "for one single day" in the U.S. But on April 16, Svetlana stepped off Swissair Flight 121 at Chicago's O'Hare airport. "I had to leave for a while to realize, 'Oh, my God, how wonderful [America] is,' " the erratic Alliluyeva explained later.

With daughter Olga happily reinstated at the British boarding school from which she had been yanked in 1984, Svetlana and a family friend drove 200 miles to Spring Green, Wis., where Alliluyeva had lived during her brief marriage to American architect William Wesley Peters, 73. Tired but elated, she slipped into seclusion at a house owned by longtime friends Derry and Robert Graves. Later she could reflect at leisure on her 18 months in the Soviet Union—and on how it all went wrong.

By Svetlana's account, her impulsive return home had been prompted by maternal longings. She had moved to Cambridge, England from Princeton, N.J. in 1982 in search of a "better life" and a strict school for the spirited Olga. There she began to yearn for the son and older daughter she had left behind in Russia and the two grandchildren she had never seen. Joseph Morozov (now a physician) had been 22 when Svetlana defected; his half sister Yekaterina Zhdanova was just 17. Svetlana had spoken to neither for many years, but just before Christmas 1983, a phone call from Joseph raised her hopes for a reconciliation. The following August, Svetlana was notified that her son was seriously ill in a Moscow hospital. She petitioned the Soviet Embassy in London for visas and abruptly informed Olga that they were going to Moscow.

Olga was a thoroughly Western child, born in Marin County, Calif. and steeped in pop culture to the extent that school friends called her "Chrissy," in honor of the Three's Company character. Leaving England meant leaving the progressive Friends' School where she was thriving. Upstairs neighbor Peter Mansfield remembers hearing Olga shouting, "Why didn't you tell me? Why didn't you consult with me?"

Two days later Olga (who spoke no Russian) found herself in Moscow for the vaunted meeting with her half brother. Things soured almost immediately. Remembers Svetlana: "I imagined that I am really very much still loved and wanted. Well, that was really not quite so." She quarreled bitterly with Joseph, and Yekaterina refused to meet her. "Very quickly, in a month's time, we realized that really nobody needed us there. That was the major shock...and for Olga too, because nobody was interested in her at all. We both felt low."

Moscow itself was another disappointment. "Life was no easier [than in 1966]," Svetlana says. "After being away, I disliked it tremendously. I didn't feel at all that I was born there. It has become a huge city with ugly modern buildings."

With Olga, she moved to Tbilisi, in Soviet Georgia, the republic where Stalin was born. But life in the provinces proved no less difficult. Alliluyeva lamented the dearth of food and clothing and found herself almost isolated. "Only a few former classmates, my university friends and people like that, showed some warm feelings," she says. "Otherwise, everybody was terribly embarrassed. They didn't know how to treat us."

By the end of the year both she and Olga wanted out. In December 1985 Stalin's daughter wrote Soviet leader Mikhail Gorbachev to ask for permission to leave the country once again. Finally, she says, the Soviets realized "there was no other way. I think they just preferred to have me out."

For Olga's mother, the future, as always, is an open question. Alliluyeva's first book of memoirs, 1967's Twenty Letters to a Friend, netted her $1.5 million and a batch of favorable reviews. She conceivably could use her latest exploits as grist for another book. One thing seems certain: For a woman who believes "a better life" is always just around the corner, the troubled quest is far from over.