The woman was arrested in March next to her submerged motor vehicle, in the presence of her children, all aged under 12.
She appeared via video link in the Melbourne Magistrates Court on Wednesday and was supported by her parents in court.
The mother had been in the grips of a severe mental health breakdown at the time, the court was told.
A psychiatrist found the woman had been suffering a "severe and debilitating" form of obsessive-compulsive disorder, which was compounded by a pre- and post-natal depressive episode around the time of the alleged incident.
Her defence lawyer argued there were comprehensive treatment and support options in the community and flagged a potential mental impairment defence.
Her mental health issues had partially resolved, Tim Marsh said as he warned of treatment delays in custody.
"(She) and the community are best served on bail and her being able to access rehabilitation services," the defence lawyer said.
The prosecution accepted the woman had no prior criminal history.
But it maintained concerns there had not been a more recent update on her mental state.
"If released, if she regresses again, there is a possibility she might regress or engage in similar behaviour or be a threat to herself," Fraser Cameron told the court.
Magistrate James Henderson said the allegations were serious and found the prosecution's case was strong.
He dismissed the woman's bail application.
She was remanded in custody ahead of a Supreme Court directions hearing on October 12.
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