A mother smothered her disabled twin sons with a nappy before killing their older sister and then tried to kill herself while suffering from depression, a court has heard.
Tania Clarence, 43, has admitted responsibility for the deaths of Olivia, four, and three-year-olds Ben and Max at their home in New Malden, southwest London, during the Easter holidays.
She was excused from court by Mr Justice Sweeney after she became too upset as details of the "grotesque" discovery of the twins' bodies were read out.
Her husband, investment banker Gary, remained inside the courtroom with other family members.
Zoe Johnson QC, prosecuting, said all three children suffered from the condition SMA type 2, a life-limiting genetic condition which leaves children with little or no control of their movement.
Ms Johnson said had the Clarences known the twins had the condition before they were born prematurely on a family holiday in Portugal, they would have agreed to abort the pregnancy.
She told the court Mr Clarence took their eight-year-old daughter on holiday to South Africa on Friday 18 April, leaving the defendant with her other children.
"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," she said.
The court heard the killings took place sometime between midnight and 3am on 22 April. The two boys were smothered first with a nappy.
Ms Johnson added: "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."
The family nanny, Jade, was called by Clarence's mother after she could not get in contact with her and went to the house with a friend, Daniel Magagnin, and a pastor.
They found Clarence in a bedroom with a towel.
Ms Johnson said: "Daniel asked Mrs Clarence if she wanted him to pray for her, she told him to go and she was a private person.
"Mrs Clarence started to say 'it's too late, it's too late, there's nothing you can do to help them'."
The nanny's friend noticed blood on Clarence's wrist and called 999. He then discovered the bodies of the twins in their room.
Ms Johnson added: "It was such a grotesque sight Mr Magagnin could not bring himself to look for Olivia as he was instructed to do by the emergency operator."
The court heard Clarence handed her nanny a letter which said "I could not carry on" and describing Jade as "an amazing person in our lives over the last few years".
It also read: "Without you I most likely would have done this a lot sooner."
The Old Bailey heard that Clarence was "under intolerable strain" from all the medical appointments the three children needed. In 2012, she told doctors she did not want to see her children's suffering prolonged.
In October, the Crown Prosecution Service accepted Clarence's guilty plea to the manslaughter of her three children on the grounds of diminished responsibility.
Mr Justice Sweeney is expected to hand her a hospital order at a later date.
SMA type 2 means children cannot stand unaided and are vulnerable to respiratory infections.