A case statement tendered to the ACT Supreme Court says the Canberra woman, whose name is suppressed, was involved in "tumultuous divorce proceedings" between 2016 and 2019.

She allegedly prevented the children's father from seeing them for a year during this time, but he eventually received 30 per cent custody of the children.

Court documents say that following Family Court proceedings, the woman was ordered to pay the man a $175,000 settlement, but failed to pay the first installment of $25,000.

Prosecutors allege the woman, "extremely unhappy" with the orders, made it clear she would do "everything possible" to avoid being forced to give up her house in order to meet the terms of the settlement.

She was also "highly possessive of the children" and decided for those reasons to burn the house down with the children inside, prosecutors say.

Just before 6am on July 21 last year, she allegedly disconnected the smoke alarms in her suburban Tuggeranong home and lit a couch and linen cupboard on fire.

"She returned to the children's bedroom and laid down crying," prosecutors allege in the case statement.

The children, a boy aged five at the time and a girl who was then six, are said to have woken as smoke filtered into their room. They found it difficult to breathe and cried out for water.

When a neighbour knocked on a window in an attempt to help, the woman allegedly told the children to stay calm and lie down.

Firefighters arrived to find the woman and children unconscious in the house.

All three required CPR and were airlifted to Sydney hospitals to be treated for smoke inhalation, with the woman and boy placed in induced comas to assist their recoveries.

The case statement says the boy also suffered superficial burns.

Emergency services found there was no indication anyone had tried to escape the burning house before being rescued.

The woman was charged with arson following the fire, and was refused bail.

She pleaded not guilty, but the charge was replaced in January by two counts of attempted murder and two back-up charges of arson with intent to danger life.

Her lawyers have indicated that she will also plead not guilty to those counts and proceed to trial.

Having spent nearly nine months in custody on remand, the woman applied for bail in the ACT Supreme Court on Friday.

Defence barrister Steven Whybrow said the woman suffered from asthma and type 2 diabetes, and was therefore at a greater risk of becoming severely ill if she contracted COVID-19.

He said the woman should be granted bail for reasons including that jails like Canberra's Alexander Maconochie Centre required inmates to live in close proximity, making "social distancing" difficult.

He said she had received mental health treatment and counselling while on remand, and could continue these if granted bail.

Mr Whybrow proposed bail conditions including that the woman live with a friend of nearly 40 years in Curtin, report to police daily, and not contact or be within 100 metres of her children or their father.

But Crown prosecutor Anthony Williamson said the woman presented an unacceptable risk to those people.

He said the case against the woman was that she had failed in a murder-suicide attempt, spurred on by "a pathological hatred" of the children's father.

Mr Williamson said if the prospect of ending her own life had not stopped the woman trying to harm her children then, there was no universe in which "a piece of paper" containing bail conditions would prevent her trying to do it again.

He also said the children's father had been "petrified" on Thursday when told the woman was applying for bail.

Justice David Mossop said the woman was required to demonstrate special or exceptional circumstances in order to be granted bail.

But the judge said it was unnecessary for him to determine whether the COVID-19 pandemic had created such circumstances for the woman, because she should not be granted bail anyway.

Justice Mossop said the nature of the allegations, the strength of the case against the woman and the unacceptable risk she would present if released justified the refusal of bail.

The matter is listed for a pre-trial callover next month.