The unemployed man faces two charges of causing bodily harm while driving over the legal alcohol breath limit, driving while disqualified and failing to stop when someone was injured.
Judge Sharon McAuslan said forensic evidence showed the car he was allegedly driving was speeding at 75-94km/h on a suburban road last Thursday night before it hit a curb and two girls walking along the pavement.
The girls were thrown over a fence and the car came to a stop after smashing through the fence, she said.
Judge McAuslan said once the car stopped, the driver made no attempt to assist the girls: "Instead you accelerated heavily in an attempt to flee."
That was unsuccessful so he jumped out of the car to try to flee on foot but was caught by members of the public.
The crash caused "life-threatening injuries" to the two young girls, she said.
Defence lawyer Hermann Retzlaff said the summary of facts spoke of an "unknown reason as to why [the accused's] vehicle swerved causing the event." He said a van had turned on the road, "causing the accident".
Judge McAuslan denied an application for bail and remanded the man in custody.
Police prosecutor Ellie Mafi said further charges could be laid.
The man's sister and mother supported him in court. His wife was taking care of the couple's four children, aged from 4 months to 11 years, said Mr Retzlaff.
Outside the court, Mr Retzlaff said his client had asked that he pass on an apology to the families of the girls, as he had not been legally allowed to contact the families.
"Downstairs he did say to me that he wanted to issue an apology to the complainants and their families for what's occurred, and that he apologises for what took place and what happened.
"At the moment he's feeling what I would describe as obviously remorseful for what's occurred, and at the same time there is a desire to let his family know that he will be able to explain everything to them."
He had intended to organise a meeting of the extended family to explain what had happened, but would now have to organise this without his client because he was in custody.
"The next 48 hours will be difficult, so it may well be just me going down and taking the message to them to explain fully. I don't think they understand, but what he wants them to know is that he's sorry."
Outside the court, the accused's sister said the family had spoken only briefly to him while he was in police custody.
"He's just devastated, not only for his family but for the other families."
