In a ruling reported for the first time Monday, High Court judge Peter Jackson said the mother had behaved in "a wicked and selfish way" that almost defied belief.
The judge said the woman, an American divorcee living in Britain with three adopted children, hatched the plan after she was prevented from adopting a fourth.
The scheme involved getting her oldest daughter to inseminate herself with syringes of sperm purchased over the Internet from a Denmark-based company, Cryos International.
Jackson said the daughter, identified only as A, "became pregnant at the mother's request, using donor sperm bought by the mother, with the purpose of providing a fourth child for the mother to bring up as her own."
In his ruling, the judge quoted the teenager as saying said she was shocked by the suggestion, but thought, "If I do this ... maybe she will love me more."
"My mum is a very determined person and she does her best not to let anything get in her way if she wants it," the teenager added.
The judge said the mother also made the teenager use douches of vinegar or lemon and lime juice in hopes of increasing her chances of having a girl.
The judge said it was likely but not certain that the daughter soon became pregnant and suffered a miscarriage. After six more attempts with the donor sperm, she gave birth to a baby boy in July 2011, when she was 17.
But midwives at the hospital became alarmed by the odd behavior of A's mother. Her daughter wanted to breastfeed the baby, but her mother said: "We don't want any of that attachment thing."
The hospital alerted the authorities, and the children were taken into foster care. The mother is now serving a five-year jail term for child cruelty.
Details of the case were heard during proceedings at the family division of the High Court over the children's future last year. They were reported for the first time Monday after several British media organizations, including the publisher of The Guardian newspaper, challenged reporting restrictions.
A court order bars identifying the family members in order to protect the children.