A mother accused of stealing her two children who disappeared from Townsville four years ago has been denied bail after appearing in the Brisbane Magistrates Court.

The 45-year-old was arrested on Friday in Taree on the New South Wales mid-north coast and extradited to Queensland where she was formally charged with two counts of child stealing.

The mother allegedly took the two 11-year-old sisters from outside their Townsville school in 2014, when they were aged seven, after their parents' marriage failed.

Outside court, the mother's lawyer, Tony Kimmins, said his client would apply for bail in the Supreme Court in Brisbane.

"The only thing I've been asked to indicate is that we have instructions that she will apply for bail in the Supreme Court, but effectively appealing the refusal of bail this morning," he said.

"That's all I can really say at this stage."

Police claim the woman and her children were living "under assumed identities" and allege the mother had multiple Medicare cards in her possession when she was arrested.

But Mr Kimmins told the court the cards had not been stolen and belonged to real people.

"I'm not suggesting she was using her real name all the time, but there is a real question of allegations of false identification and my instructions are that she has never applied for false identification," Mr Kimmins said.

Mr Kimmins told the hearing if granted bail, his client would live with her parents in Townsville and report to police seven days a week.

He offered a $25,000 surety and said she would not attend any airports or travel further south than Home Hill.

"She intends to see this through … and wishes to reconnect with her children," Mr Kimmins said.

Senior Constable Wade Domagala opposed the application for bail.

"There is a unacceptable risk that she will fail to appear," he said.

"She has eluded police and authorities for just over four years now."

The matter has been adjourned to the Townsville Magistrates Court for later in the month.