But a lawyer for the boys' grandparents, Dale Brooks, maintained the tragedy would not have happened were it not for serious failures by authorities, calling the denials "fatuous nonsense". 

Mr Brooks said the woman was not given proper housing when she was released from prison a month ago, after serving a sentence for breaking and entering.

She came to live in the south-west NSW town of Deniliquin in a caravan on the property of her mother, who had assumed care for the children, aged nine and five.

The grandmother last year took out an apprehended violence order against her daughter, which forbade her from approaching after drinking or taking drugs. 

"If she didn't live at that property, she would never have had access to a car for starters and she would never have had access to snatch those two little fellers," Mr Brooks said. 

He has also alleged the Department of Corrective Services failed to advise the grandmother of her daughter's "mental decline" after an assessment and did not "take steps to protect our client and her grandchildren".

The body of the five-year-old was recovered from the river near Moama on Saturday while his brother remained in hospital. The woman, bail formally refused, did not appear in local court to face a charge of attempted murder. She is expected to face further charges.

Corrections Minister David Elliott said he expected a "full briefing" on his department's handling of the case. 

The department in a statement said it was still investigating some claims but "strongly denies most of the serious allegations against its staff".​

"We could not have foreseen this shocking outcome," said acting Assistant Commissioner for Community Corrections Michelle Micallef.  "It appears our staff took reasonable steps to put appropriate services in place and to make alternative accommodation arrangements."

The department said accommodation in the area was "extremely restricted". It is understood the woman attended at least one drug and alcohol counselling session at a local clinic.

According to support services, many women find themselves homeless and without medication on their release from jail.

Chief executive of the Women's Justice Network, Lana Sandas, called it a "dangerous gap" in which reoffending was more likely.

Sixty to 80 per cent of female prisoners were homeless on their release and 84 per cent of the network's clients suffered mental illnesses, not including depression and anxiety, Ms Sandas said.  

"There is absolutely no link between Justice Health and the public health system in the community," she said. 

Mindy Sotiri, program director of the Community Restorative Centre, said most women entered prison on a "conveyor belt" of disadvantage and confronted a confusing array of services on release. 

Many services provide counselling for drug and alcohol problems or mental illness but not both and many bar patients with a history of violence, which is given a broad definition. 

"There is a big gap in the service landscape," Dr Sotiri said.