Guode and her daughter Aluel, who was 5 at the time, survived after being pulled from the water after the crash on April 8 this year.
Several family members, including a man understood to be the father of the dead children, packed the court for Guode's brief filing hearing.
She was remanded in custody to reappear on December 8.
Prosecutor Tim Bourbon told the court CCTV footage had captured the street near the incident, and "certain things", such as driving.
Zolis asked that Guode be kept in protective custody, in light of the allegations against her, and asked that she get professional cost support.
"The enormity of the charges and the inability to see her children will have a substantial effect on her," he said.
"She has never been incarcerated before, she's never been in trouble in her lifetime."
Outside court, and flanked by the family, Zolis reiterated how devastated Guode was.
"She wanted me to tell people, especially her family and the family of her children, that it has been an extremely, extremely painful experience," he said.
Zolis said it was too early to give any indication of a plea, and bail would have to be looked at.
He said the father of Guode's dead children was "holding up".
"It's been a traumatic situation for him," Zolis said.
"What I can say is, he supports Akon."
Zolis said Guode's family and friends loved and respected her.
"I believe there were even more people that wanted to come along today."
- AAP
