The incident happened on October 24 last year when the mother put her child on to the school bus with his siblings around 8.30am, she said.
Tuck-Lee, who was filling-in for a regular colleague, dropped the older children off at school, but instead of driving to the nearby primary school to drop the two remaining children off, he drove back to the depot.
In his defence, he said the boys were not sat in the pre-school section and had hidden down at the back of the bus.
For the next six hours, the pair sat on the coach, with the mother of one of the boys saying they were too afraid to eat their lunches or drink water because eating and drinking on the coach is not normally allowed.
Another driver eventually found the pair at 2.30pm when they were taken back to the school and handed back to their parents.
The mother of one of the boys said her son was covered in sweat, smelled like urine, and his face was pale and splotchy from crying.
She added that the school failed to tell her that the boy had not turned up to classes.
Tuck-Lee is due in court again on February 16 to seek a lesser penalty. He says he is not disputing the fine, but wants a criminal element of the charge dropped because it is affecting his other business as a contract mechanic.