Patricia Joan Smith, 42, fronted Parramatta Local Court for the first time on Saturday in a brief hearing where she did not apply for bail.
Police charged Smith, the mother of 11-year-old Russell and nine-year-old Ben Smith, with two counts of domestic violence-related murder after their bodies were found at their Faulconbridge home on Tuesday.
Emergency services had been called to the house following welfare concerns for a woman and two children, with the boys' father allegedly finding their bodies on the same day.
Lawyer Paul McGirr says family members are "really hurting" after the death of the two boys. (Dean Lewins/AAP PHOTOS)
NSW police said Smith was also found at the scene with stab wounds and was taken to hospital in a critical but stable condition.
She was released from hospital on Friday and taken to Parramatta Police Station where she was charged.
Following the brief hearing on Saturday, Smith's lawyer Paul McGirr said family members were "really hurting".
"Parents, grandparents and the like, and we'd ask that everyone respect that privacy because, as I said, right from emergency services who had to attend the scene ... there'd be a lot of people out there that have been subjected to this," he told reporters outside court.
The father of the two boys has called for privacy saying their deaths had caused pain and distress. (HANDOUT/NSW POLICE)
The boys' father Nick Smith, who does not live at the Blue Mountains home, this week expressed disbelief at the tragedy while also calling for privacy.
"The loss of our two beautiful boys has caused unimaginable pain and distress," he said in a statement.
"Russell and Ben were happy, funny, outgoing boys and were very much loved by their family and friends."
Magistrate Michael Stoddart remanded Smith in custody until her next committal appearance on November 8.
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