The former prime minister felt guilty that she had failed as a mother, had a chilly relationship with her daughter and was rarely, if ever, physically affectionate, according to Mr Aitken's latest memoirs.
He also claims that Carol believes her brother Mark has received "an over-large slice of the inheritance cake" and details recent clashes with her mother.
Carol Thatcher, who won ITV's I'm a Celebrity... Get Me Out of Here! last year, is alleged to have stormed out of the former premier's London home saying, "Lady Thatcher, you were a great prime minister but you are a terrible mother".
Mr Aitken, jailed for perjury in 1999, had a two-year relationship with Carol Thatcher that he ended just after the Conservatives won power in 1979.
Writing in detail about his friendship with the Thatchers for the first time, Mr Aitken reveals intimate details of their family life. "She and her mother had a tense relationship, with more chill than warmth. I had the impression that Carol admired Margaret from a distance, but did not enjoy being close to her," he writes. "Carol never had a good word to say about Mark."
He denies, however, that Lady Thatcher favoured her son, revealing that she once changed the date of a crucial parliamentary vote so that Mr Aitken, then an MP, could take her daughter skiing.
The disgraced former minister says Carol sometimes set out to deliberately provoke her mother, demanding on one occasion if she knew the prices of everyday foodstuffs.
The then leader of the Opposition - who was to win an election partly by emphasising inflation-led price rises - failed "several of the questions" in her daughter's shopping quiz.
But it is his revelation on the family's internal dynamic that caused greatest controversy yesterday, as family friends sought to excuse Lady Thatcher's behaviour. Gerald Howarth, the Conservative MP for Aldershot, said: "I don't think anybody has any idea of the pressures on families in the highest positions of public life. The Queen has seen three of her four children in failed marriages so I think you have to see the Thatchers in that context." He said Sir Mark Thatcher was "splendid" and had always been "a model of courtesy".
Mr Aitken's memories of the former prime minister's son are surprisingly warm, revealing that Sir Mark had written to him inviting him on an all-expenses-paid holiday to South Africa after he was released from prison.
It was Sir Mark, Mr Aitken says, who rushed to his mother's bedside after a recent stroke. "One way and another Carol's alienation from her mother is almost as bad as her alienation from her brother," writes the former minister in the book, Heroes and Contemporaries.
Another family friend said that he was "not surprised" to learn of recent clashes between Lady Thatcher and her daughter. "The truth is they have never been close." The friend added that Mr Aitken's revelations would be met with disdain. "It does seem rather grubby that he's cashing in after all these years," he said.