Tania Clarence smothered her severely disabled twin sons with a nappy before killing their older sister after her social worker was changed.
Clarence, 43, appeared at the Old Bailey on Friday for a sentencing hearing, having previously admitted responsibility for the deaths of Olivia, four, and three-year-old Ben and Max at the family home in New Malden, south west London.
The court was told how she had been struggling to cope with the mental and physical demands of her children's illness and had told doctors that had the family been living in their native South Africa, they would have 'gone to the top of a mountain and died'.
However she struck up a good relationship with her social worker, Suzi Holley, and was making progress, when Kingston Social Services, made the 'ill-conceived' decision to reassign her another less experienced worker because they felt she had become 'too close' to the family.
The court heard that Mrs Holley was so outraged by the decision that she resigned soon afterwards.
Zoe Johnson QC for the Crown explained how all three of the children had suffered from the life limiting, muscle weakening condition, SMA type 2.
She said had the Clarences known about the condition before the twins were born prematurely on a family holiday to Portugal, they would have agreed to abort the pregnancy.
Outlining the events leading up to their deaths, she said Clarence's husband had taken their eight-year-old daughter on a holiday to their native South Africa on Friday April 18, leaving the defendant alone with her other children.
She said Clarence had given the family's nanny, known as Jade, the day off.
Ms Johnson said: "We suggest that the defendant took this opportunity to end the lives of her three disabled children, although it was right to say her settled intention was only formulated on the Monday.
Ms Johnson went on: "She smothered the boys first whilst they were sleeping using a nappy so they would not smell her.
"She found it much harder to kill Olivia, and wrote a letter to her husband in the time between killing the boys and killing Olivia."
But Ms Johnson said the decision to move Mrs Holley off the case and reassign a different social worker to the family at a time when it was clear Mrs Clarence was struggling to cope, had been 'ill-conceived'.
She said: "It appears that Miss Holley developed a reasonably good working relationship with the family, but in February 2014 she was suddenly replaced by a young and less experienced social worker, Sarah Daws.
"This disruption was in part because the social services department thought that Ms Holley had got too close to Mrs Clarence and her reaction was to resign soon afterwards.
"Ms Daws became the Clarence family social worker just six months after she joined Kingston social services. With hindsight that was an ill-conceived decision by the social services department."
The children's bodies were discovered by their nanny, who had been given the day off on the day in question, but had been asked to look in after family became concerned.
The court heard they were tucked into their beds with toys arranged around their heads.
Last month the Crown Prosecution Service accepted Clarence's guilty plea to the manslaughter of the three children by reason of diminished responsibility.
Mr Justice Sweeney reserved sentencing until tomorrow (November 18).