"These children are very lucky," she said.
The female passenger was also uninjured and the driver suffered serious injuries believed to include a broken leg.
When emergency services arrived at the scene, the man became "very aggressive".
"He was hostile towards ambulance staff," Const Manning said.
"It was appalling the way he was speaking to them."
The man was yet to be charged, but charges other than driving offences were also likely, she said.
The group had left a Lock St address and were travelling towards the motorway when the man lost control of the 1995 BMW 318I.
Alcohol and speed were believed to be factors in the crash.
Richard Abernathy was visiting his mother's house when he heard the crash.
"It was just an almighty bang," Mr Abernathy said.
"It made the house have a wee bit of a shudder."
He ran out to the street, fearing the worst.
"The mother was shaken up; she was petrified because of the kids," he said.
The driver was "scared and anxious" and still trapped in the car, as were the children.
Mr Abernathy's mother said the road was notorious for crashes.
There had been "three quite bad" crashes near her home during the past year.
"They speed here something ... wicked," she said.