Justice Sweeney said in his ruling that she had been “overwhelmed”.
Clarence, 43, pleaded guilty to 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, who suffered from the muscle-weakening condition SMA type-2, were found dead, tucked into their beds with toys arranged around their heads as if on a “bier” lying in state.
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 her alone with her other children, having given the nanny a day off.
Clarence wept uncontrollably in the dock last week as the “grotesque” details of the killings were read out by the prosecution.
Her husband, investment banker Gary, who has supported his wife throughout, also looked visibly distressed.
All three of the children suffered from the muscle-weakening condition SMA type 2. Had the Clarences known before the twins were born, they would have agreed to abort the pregnancy.
Prosecutor Zoe Johnson QC told the court: “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.”
When police arrived at the house in Thetford Road, a female police officer found the twins, Ms 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 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”.
The mother-of-four left a series of notes, including one to her nanny and her husband.
The court was told Clarence repeatedly clashed with doctors during a long history of the children’s medical treatment in and out of hospital.
Clarence’s attitude was that their quality of life was more important than its length and she preferred to opt for palliative care over more invasive treatment.
On one occasion, she said: “Gary and I do love our children just not in the way you want us to.”
In May 2011 a doctor noted that Clarence was “seriously over-stretched/under intolerable strain” from all the medical appointments.
At the end of 2012, she told medics that 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”.
She also admitted to medical staff that she was suffering from depression on more than one occasion, yet did not follow through with any professional help.
Just before the killings, Clarence had been resisting agreeing to a gastrostomy for Olivia that doctors had urged because of fears that she was underweight.
The dispute also coincided with the appointment of an inexperienced social worker from Kingston Borough Council who replaced a woman who had resigned in disgust after being moved off the case because she had got too close to the family, the court heard.
At a meeting on March 24, the new social worker presented Clarence with a list of subjects for discussion including gastrostomy, physiotherapy routines, spinal surgery, her mental health – all of which she found “overwhelming”.
In April, Mr Clarence urged “tact” as he finally agreed to a gastric button for Olivia, but at the same time, Kingston social services called a meeting to discuss the possibility of instituting child protection measures.
The social worker ignored his plea and during a second visit on April 16 without Mr Clarence being present she suggested to Clarence a gastric button for the twins next. Days later, all three children were dead.
Ms Johnson asserted: “Tania Clarence’s rational belief that she didn’t want to prolong her children’s lives became distorted into an irrational decision to kill her disabled children, a decision she had formed well in advance of the killings.”
Defending, Jim Sturman QC said: “You are dealing with a case where there is no evidence at all that Mrs Clarence would have harmed a hair on their head but for the illness she suffered.”
Clarence had “adored” her children, but the problems of caring for them were “almost unimaginable” considering they were unable to feed themselves, walk, or hold themselves up.
He said it was not right to say Clarence would have preferred “nature to take its course” when the parents just wanted their children to be happy.
Sweeney had described the case as “extremely difficult”.