The footage, caught on a dash cam, was recorded on the junction of Newstead Lane and Garmil Head Lane in Fitzwilliam, opposite the Catchpenny pub, at around 4pm on Tuesday, March 6.
It shows the small silver Vauxhall Viva attempting to negotiate a turn but ploughing into the Vauxahll Zafira people carrier heading in the opposite way.
The driver, followed by his three passengers, can then be seen running off.
Witness Richard Lord, a painter and decorator from Hemsworth, whose camera recorded the footage said: “I’d been coming home from Wakefield and was waiting on red at the traffic lights.
“The car should have been waiting at the red light but it came round the corner and you could hear the bang as it hit the Zafira which had a mother her child inside.
“After they ran off I pulled up on the grass verge and was in two minds of whether to chase them but went to see if the woman was okay.
“She was a bit shaken and she think she broke her finger and her little boy was shaken up as well. They went to hospital but I think they were okay.
“All the airbags in both cars went off. It looks like both cars might be written off.”