The woman, who cannot be identified, was arrested in March after she was found next to her submerged car in the presence of her children, all aged under 12.
She was subsequently charged with 11 offences including five counts of attempted murder.
Prosecutors allege the woman drove her children off a boat ramp and into a creek on March 1.
It's alleged she locked the vehicle's doors and drove at speed into the body of water, placing her children in danger of death and serious injury.
She is also accused of forcing her children's heads under water, placing them in danger of death.
The woman made a bid for bail in the Victorian Supreme Court on Thursday, after an unsuccessful attempt in the magistrates court in September.
Her barrister Tim Marsh argued there were exceptional reasons for bail, noting a recent psychiatric report had raised the availability of a mental impairment defence.
The woman had a severe and debilitating form of obsessive compulsive disorder and severe pre- and post-natal depression, Mr Marsh said.
At the time of the alleged attempted murders, the woman was experiencing an acute mental health episode, the barrister said.
The consideration of a mental impairment defence had led to delays in the case as prosecutors sought to obtain their own psychiatric opinion, Mr Marsh said.
The woman was no longer in an acute mental state after being treated at a secure forensic mental health facility when she was first arrested, the barrister said.
But since her discharge from the hospital in April, she had only received "fairly limited" support in custody, Mr Marsh said.
He told the court if the woman was bailed, she would obtain a mental health plan from her GP and then see a psychologist.
She was also planning to live with her parents and not have any contact with her three children, Mr Marsh said.
The barrister argued the woman was not a risk to the community at large and the risk she posed to her children could be mitigated.
"This offending is entirely specific to the very unusual circumstances of March this year," Mr Marsh said.
Prosecutor Diana Karamicov opposed bail, arguing it remained unclear how the woman would receive mental health treatment in the community.
The woman's husband had also raised concerns about attempts she might make to contact the children, Ms Karamicov said.
Justice Amanda Fox will hand down her bail decision on Friday.
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