Tania Clarence admitted killing 4-year-old Olivia, and 3-year-old twins Ben and Max, but pleaded diminished responsibility.
Clarence allegedly smothered them at the family's London home in April, before attempting suicide.
Her husband Gary was in the couple's native South Africa at the time.
The children all had type 2 spinal muscular atrophy, a condition which affects muscle strength.
Defense lawyer Jim Sturman said that for Clarence, "caring for three children with this condition was exhausting, distressing, debilitating and turned out to be overwhelming."
Prosecutor Zoe Johnson told a hearing at London's Central Criminal Court that Clarence "killed her three children because she wanted to end their suffering."
Johnson said prosecutors accepted Clarence was depressed, which amounted to an "abnormality of mind."
Clarence is due to be sentenced Nov 14 and is likely to be sent to a psychiatric hospital.
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