Patricia Joan Smith is accused of killing her two sons Russell, 11, and Ben, 9, at their Blue Mountains home west of Sydney in September 2024.
The 44-year-old appeared by videolink from Silverwater prison before the NSW Supreme Court on Friday to be arraigned.
Smith avoided looking at the camera in her cell, instead looking down at the floor and back at the door with her hair covering her face as she pleaded not guilty two charges of domestic violence murder.
Justice Peter Hamill heard crown prosecutors had consented to a verdict of not guilty because of mental health impairment.
A hearing has been scheduled for June 2 where another judge will hear arguments about why Smith was not criminally responsible because of her mental state.
Earlier on Friday, barrister Madeleine Avenell SC referred to her client's difficulties when asked if she understood what it meant to be arraigned.
""I'm not sure how receptive she will be but she does understand," Ms Avenell told the court.
The exact details of Smith's mental health impairment have not been divulged in court.
At a funeral in September 2024, the boys' father Nick Smith pleaded for his sons to be remembered by their friends.
"One thing I do ask is, every time you come back to the Blue Mountains … please go visit the boys (and) tell them all the great things you've done since you last saw them," he said in a eulogy.
"Make sure they always live inside all of you."
A community fundraiser run by the boys' school helped raise over $32,000 to help cover funeral costs.
Mr Smith found the bodies of his sons at their Faulconbridge home on the day they were allegedly murdered.
NSW Police said his ex-wife was also found at the scene with stab wounds and was taken to hospital in a critical but stable condition.
Lifeline 13 11 14
beyondblue 1300 22 4636
Kids Helpline 1800 55 1800 (for people aged 5 to 25)
27°C