A judge has called for more evidence about the woman's mental health and history of violent offending after noting she later downplayed the tragedy involving her own child, describing it as "one mistake".
In the latest incident, the woman approached the nine-year-old girl and her grandmother while they were sitting at a bus stop in Sydney's southwest in December 2022, grabbing the girl by the arm and attempting to pull her away.
The grandmother, who was assaulted during the incident, fought the woman off before the latter fled into a nearby unit complex.
The woman, who cannot be identified for legal reasons, pleaded guilty to attempting to take a child, common assault and resisting arrest.
During a sentence hearing in Sydney's Downing Centre District Court on Wednesday, Judge David Wilson raised concerns about the woman's risk to the community if she were to be released.
The woman has a history of schizophrenia and has previously been hospitalised for drug-induced psychosis, the court was told.
Judge Wilson raised issue with the now 49-year-old's response to the death of her daughter in October 2003, over which she pleaded guilty to manslaughter and was sentenced to five years in jail.
Regarding her two other children being placed in care, the woman was quoted by the judge as saying, "because you make one mistake in your life".
"She very much downplays it," Judge Wilson said.
The woman placed her daughter in the scalding hot bath which left her with serious burns to around 75 per cent of her body.
She then placed her baby on a change table, dried her using a bath towel and rubbed her skin with cream and shampoo.
A neighbour in an adjoining unit told police they heard the "loud, continuous screeching and crying of a baby" which continued for around one to one-and-a-half hours.
About midnight, the woman left the unit with the baby in a stroller, attempted to buy drugs and arranged with a passing motorist to perform a sex act in exchange for money.
Police later found the woman and her dead baby.
Judge Wilson adjourned Wednesday's sentence hearing to organise further evidence about the woman's ongoing mental health and facts regarding her criminal history.
"I'm concerned about releasing her into the community given her history," he said.
The mother of the girl she tried to abduct called for "considerable action" following the crime.
In a victim impact statement, she said she had lost faith in the justice system as it allowed a person with a history of violent acts to be given a second chance only to harm another family.
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