Christopher Lewin, 19, changed his plea to guilty to the manslaughter of Adele Thompson, 12, and Daniel Davies, 9.
As Liverpool Crown Court heard how the bodies of the two children were thrown through the air when the red Mazda MX3 spun out of control, two men vaulted from the public gallery.
The men - believed to be relatives of the victims - ran at the dock, shouting abuse.
Lewin and David Nnah, 21, his co-defendant, were taken away by prison officers as police and court officials struggled to restrain the two men. Both were eventually led from the court, still struggling.
The judge, Mr Justice Hidden, said: 'Everyone in this court realises what some of you must be feeling but these proceedings have to go on and they will.'
As the accused were led to the cells after the hearing, Adele's aunt, Pat Thompson, shouted: 'Why did you take her away from us? Killers, child killers] He's been in jail 10 months - she's in a cemetery.'
Rodney Klevan QC, for the prosecution, told the court how Lewin and Nnah, 21, took the car from outside a Liverpool hotel on 30 October last year. They crashed into a parked Volvo and almost ran over a passer-by as they drove away.
Other witnesses saw the car go through a red light before racing along Toxteth's busy Granby Street at up to 70mph. Mr Klevan said Lewin had taken the car to the street - just over 100 yards from his home in Mulgrave Street, Toxteth - 'to show off'.
The car raced to the end of Granby Street, turned and came back, weaving through parked cars at up to 65mph, before it went out of control.
Mr Klevan said the car hit the wall of a school, struck the two children, spun round and hit a lamp post. 'The two young children died of multiple injuries. There was no chance of saving either of them.'
A third child, Christopher Nimbley, nine, was also injured. The two men ran away but gave themselves up the next day. The court was told that Lewin had been banned for 18 months for earlier offences of taking cars and driving under age. He had never taken a driving test.
Richard Henrques, for the defence, said Lewin had admitted driving at about 60mph. 'By his plea he acknowledges that that was indeed reckless to a high degree.'
Lewin was remanded in custody until 25 September, when the judge will consider social inquiry reports before sentencing him.
Nnah, of Edge Hill, Liverpool, pleaded guilty to taking the car. His pleas of not guilty to the manslaughter of the two children were accepted by the prosecution, who said he had not driven the Mazda at any stage.
He was remanded in custody until 25 September.Reuse content