Tania Clarence, 43, of New Malden, south-west London, admitted the manslaughter of three-year-old twin sons Ben and Max, and daughter Olivia, aged four, due to diminished responsibility.
The children, who all had type 2 spinal muscular atrophy, were found at their home on 22 April.
She was sentenced at the Old Bailey.
Mr Justice Sweeney told Clarence she would not be released until she had recuperated from her illness.
During sentencing he said the mother had been 'overwhelmed' by her family's situation including witnessing medical interventions and procedures she felt were unnecessary.
He told the court she had a history of mental illness and was vulnerable at the time but had been of previous good character and there was 'clear and convincing' evidence she was suffering a 'major depressive episode'.
The court heard the children were found tucked into their beds with toys arranged around their heads.
Spinal Muscular Atrophy (SMA)
- A genetic disorder that affects nerves responsible for muscle function
- It causes the muscles to waste away over time, which can lead to skeletal deformities, such as abnormal curvature of the spine, and problems walking, eating, drinking and breathing
- It is rare, affecting one in every 6,000 babies born in the UK
- However, the most common of the three forms of SMA is the most severe, and usually proves fatal in a child's first year
- Children with a milder form of the disorder can live to adulthood
- The mildest form of SMA does not usually affect life expectancy