The 47-year-old woman was arrested after allegedly attacking her children - aged 10, 13 and 16 - with a household knife on Monday.
The 10-year-old boy was stabbed twice, the 13-year-old girl three times, and the 16-year-old sustained one stab wound and a number of lacerations, police say.
Their mother, who cannot be identified for legal reasons, then allegedly stabbed herself in the abdomen three times.
She was charged with three counts of causing grievous bodily harm with intent to murder and remains in hospital under police guard.
The mother-of-three did not apply for bail and it was formally refused when her lawyer briefly mentioned the case in Parramatta Local Court on Tuesday.
The case was adjourned until May 29, leaving the mother on a path to custody on remand once discharged from hospital, pending a potential bail application.
An interim apprehended violence order has been taken out by police against the woman.
"It's a tragic case for all concerned," her lawyer Peter Guirguis told reporters outside court.
Her three children - one of whom has paraplegia - were taken to hospital after the attack and are expected to recover from their injuries.
They had been asleep in their bedrooms inside the Baulkham Hills home before the alleged attack, which woke their father.
The man was able to seize the weapon from his partner before calling police.
Footage of the scene showed one of the children being stretchered away from the house with a pink teddy on their lap.
Police said the family had no previous history of domestic violence.
Lifeline 13 11 14
beyondblue 1300 22 4636
1800 RESPECT (1800 737 732)
