A Canberra woman accused of leading police on a dangerous pursuit through a school zone is wanted in NSW over a crash that threw her two-year-old boy from the car, breaking his collarbone.

Jamie Lee Gudgeon, 24, faced the ACT Magistrates Court on Friday, seeking to be released on bail after allegedly fleeing from police at high speeds last week.

But Magistrate Beth Campbell suggested the defence would need to pull a rabbit out of a hat to get their client released from the cells.

Gudgeon is accused of fleeing from police at three different times on Thursday, with police repeatedly forced to call off the chase due to the danger to others.

At one point, the mother of four allegedly led police on a high speed chase through a school zone about 3pm on a school day.

She is also accused of speeding the wrong way through a roundabout while fleeing police, the court heard, and police say she drove directly at officers in Queanbeyan.

She was arrested the next day, after a car she was travelling in smashed into another car head-on.

That accident left her partner in hospital with serious injuries.

Detective Sergeant John Giles told the court NSW authorities had a warrant out for Gudgeon's arrest over a crash in September 2011.

Gudgeon was allegedly driving while disqualified, when she crashed into a dam.

The collision threw her son from the car and sent him into the dam, the court heard.

The boy was left with a broken collarbone, but survived the crash.

Police are also investigating a haul of suspected stolen property found in the car Gudgeon was travelling in on Friday.

The 24-year-old was identified as the driver by officers, CCTV, and by clothing found in the vehicle, the court heard.

Once Detective Sergeant Giles had finished giving his evidence, Magistrate Beth Campbell turned to defence lawyer John O'Keefe and asked: "What rabbit are you going to pull out of the hat, where's the rabbit?"

"The case against my client is quite weak," Mr O'Keefe said.

"I was just thinking it was overwhelmingly strong," Magistrate Campbell replied.

Mr O'Keefe said there was a lack of evidence identifying Gudgeon as the driver.

He said she would be able to reside at her government housing property in Theodore, despite in the process of being evicted.

Gudgeon was refused bail, and Magistrate Campbell said she would be a danger to innocent members of the public if she was released into the community.

She will be back in court on March 22.