Rayann El Houli faced Melbourne Magistrates Court on Tuesday as her bail application continued.
The 34-year-old was charged in May with travelling to a declared conflict zone, and joining the terrorist organisation Islamic State.
She voluntarily travelled to Syria in 2014, living under Islamic State rule until their defeat in 2019, Senior Constable Paul Sherlock alleged in court.
El Houli and her family were detained by Syrian forces and held at the Al-Hawl detention camp in northeast Syria for six years until September when they were smuggled out and returned to Australia.
Outlining the facts of the case, Sen Const Sherlock referred to videos El Houli had filmed of her children while they were living in IS-controlled Syria.
In a May 2015 clip, translated from Arabic, El Houli allegedly showed a video on a laptop to her toddler, appearing to feature the "mujahedin", or IS fighters, holding guns.
"What are they doing? Killing the disbelievers?" she allegedly asked.
"Yes," the child responded.
"Where does Allah put the disbelievers? In the hellfire," she allegedly said.
"In the hellfire," repeated the child.
Sen Const Sherlock said another video showed El Houli encouraging her child to "act like a mujahedin".
"How do you hold the weapon?" she allegedly asked, as the child mimicked shooting with a rifle.
"Hold it well," she allegedly repeated.
She is also accused of asking the child to show how the mujahedin "slaughter the (infidels) with the knife".
The clips were not played in open court with El Houli's lawyer Peter Morrissey SC saying she had experienced significant PTSD seeing her children in those videos.
Sen Const Sherlock also said many weapons, including guns, could be seen in the videos at the home where El Houli stayed with her sister and brother-in-law after divorcing her third husband.
He described how one video allegedly showed children sleeping in a bed with an AK-47 leaning on the wall next to them.
The lead investigator said El Houli posed an unacceptable risk of endangering the safety of the community and that of her children.
Stringent bail conditions would not allay concerns given that authorities had no information she had moved on from the radical ideology, he said.
Prosecutor Andrew Sprague said El Houli's alleged engagement and enthusiasm for IS when she travelled to Syria and supported the regime "undermined" her assertions about her initial ideology and motivations.
He said her explanation to psychologist Katie Seidler that she was just performing a role was contradicted by videos of her allegedly showing her children propaganda.Â
"Seeking to indoctrinate them?" Magistrate Brett Sonnet asked.
"Yes, Your Honour," Mr Sprague said.
Upon her return to Australia in 2025, she declined to participate in a Countering Violent Extremism program, the court was told.
But the defence countered that she had been experiencing symptoms of multiple sclerosis while juggling a "very stressful life" caring for her children.
Mr Morrissey said her activities in Syria were "very old" from 2018, and she was now focused on being a good mum.
"The protective factor is enhanced in knowing if she does something wrong, she will be arrested and separated from her children?" the magistrate asked.
"Yes, and that will damage her and the children," Mr Morrissey said.
Mr Sonnet will hand down his bail decision on Monday.
