Tania Clarence, 43, has admitted the manslaughter by diminished responsibility of Olivia, four, and three-year-old twins Ben and Max at the family home in New Malden, south-west London, over the Easter holidays.
The children were found dead, tucked into their beds with toys arranged around their heads.
After just 20 minutes of listening to “grotesque” details at the Old Bailey, Clarence became too upset and was excused by Mr Justice Sweeney.
Her husband, investment banker Gary, and other family members stayed behind in court.
Prosecutor Zoe Johnson QC said all three of the children had suffered from the muscle-weakening condition SMA type 2 and, had the Clarences known before the twins were born, they would have aborted the pregnancy.
Days before the killings, Clarence’s husband had taken their eight-year-old daughter, who is not disabled, on a holiday to South Africa, leaving the defendant alone with her other children.
Having given a nanny a day off, she decided to end their lives in the early hours of April 22.
Johnson said: “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.”
The deaths were discovered that night after a nanny, Jade, was phoned by Clarence’s mother, who had tried to contact her during the day without success.
Accompanied by her friend Daniel Magagnin and a pastor, she let herself into the house and found Clarence in her bedroom.
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.’
“Jade gave Mrs Clarence a hug. Mrs Clarence lay down and pulled the duvet over her. Daniel noticed blood on her wrist and called 999.
“He opened the twins’ door and discovered the dead bodies of the twins. It was such a grotesque sight Mr Magagnin could not bring himself to look for Olivia.”
Meanwhile, the court heard Clarence handed her nanny a letter, which read: “I’m so sorry I had to do this but I could not carry on. I also could not leave the children with Gary. It would have been too much for him.
“You have been such an amazing person in our lives over the last few years. Without you I most likely would have done this a lot sooner.”
When police arrived at the house in Thetford Road, Magagnin was hysterical as he pointed a female police officer towards the twins’ bodies.
Johnson said: “Each boy lay on his bed, on his back, with their eyes open and their mouths open.
“Little cars and toys had been placed by their heads. The covers were neatly tucked in and their arms were on top of the covers at their sides.
“Mrs Clarence had clearly placed the boys into some sort of pose, as if they were on a bier.”
A male officer found Olivia, who was also in her bed with the covers tucked up to her chin and toys placed around her.
Clarence repeatedly told the officers: “I’m sorry, I’m sorry. I killed them.”
Johnson went on to outline a long history of the children’s medical treatment in and out of hospital and Clarence’s attitude that their quality of life was more important than its length.
In May 2011, a doctor noted that Clarence was “seriously over-stretched/ under intolerable strain” from all the medical appointments and daily routine of dealing with three disabled children, adding: “One cannot underestimate practical as well as emotional difficulty this family face.”
In spring 2012, Clarence told a private psychologist she was “struggling with life” but never followed up the call with therapy. At the end of 2012, she told medics she did not want to see her children’s suffering prolonged and “if they were in South Africa they would go to the top of a mountain and die”.
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 is expected to hand her a hospital order.