Agency workers Jamie Ford, 24, and his father, Stephen Ford, 50, were working for contractor Do It Al to demolish a barn at a farm near Blandford in November 2008.
Son Jamie was using a handtool to demolish the wall when a piece came down and hit his father Stephen on the head. The HSE investigation found neither man was wearing a hard hat and Stephen, of Poole, died of his injuries at the scene.
The court heard no plan of work for the demolition was in place and Alaister Copland had no experience in demolition work of this kind.
Alaister Copland, trading as Do it Al, was fined a total of £10,000 and ordered to pay compensation to the family of £2,390 at Dorchester Crown Court in a case brought by the Health and Safety Executive (HSE) after the fatal incident.
Speaking after the hearing, HSE inspector, Helena Tinton, said: "This is a tragic case which clearly demonstrates the dangers of carrying out demolition work without suitable planning.
"There were multiple failings with this project. In addition to having no written plan for the demolition work, there was inadequate supervision and no-one on site wore head protection.
"This demolition work should have been carried out remotely using machinery with clearly marked exclusion zones in place.
"In failing to plan and carry out the demolition of this building in a safe manner a family has suffered the devastating consequences of worker contributing to his own father's death - an absolutely tragic situation."
Copland, of Queen's Drive, Moreton, Dorchester, pleaded guilty to a breach of Section 3 (2) of the Health and Safety at Work Act 1974.