Jon-Paul Prigent, 47, was pronounced dead at the scene after the tragedy on Station Lane, Old Whittington, at around 1.10pm on Thursday.
His inquest was opened at Chesterfield Coroner’s Court on Friday.
Coroner Peter Nieto said: “Mr Prigent was in a Toyota Aygo car giving a driving lesson to one of his children.
“There was a tractor which had a large trailer with a large amount of soil.
“Somehow, the trailer became detached from the tractor, rolled back and hit the side of the car where Mr Prigent was sitting.”
The driver of the Toyota Aygo was taken to hospital with minor injuries.
The tractor driver was arrested on suspicion of causing death by dangerous driving.
Mr Nieto adjourned the inquest to a later date.
Mr Prigent, of Laburnum Street, Hollingwood, worked as a programme manager.
Shocked Chesterfield residents reacted to news of the incident and passed on their condolences to the families involved.
On our Facebook page, Nick Townsend said: “We all lost a true friend and absolute gentleman.”
Derbyshire Constabulary officers want to hear from any witnesses or anyone who has dashcam footage of either vehicle before the incident. Call 101 and quote reference 610 of July 30.