Devon County Council decided not to pay for the school transport for L/Cpl Christopher Chell's children after they had to move home.
The authority previously signed up to the Armed Forces Covenant, which pledges that service families are not disadvantaged because of their job.
The council has apologised and Â£2,000 has been awarded to the family.
Previously L/Cpl Chell lived near Exmouth with his wife and five children, including Kyle who had cancer.
The Local Government Ombudsman (LGO) said the family had to move further away from their children's school because their accommodation was making Kyle's illness worse, but Devon County Council did not make allowances and refused to pay for school transport.
However, the LGO ruled the authority failed to honour its own pledge after it signed up to the covenant.
Dr Jane Martin, from the LGO, said: "Councils that have signed up to the covenant have pledged to consider the often quite unique circumstances that forces families find themselves in.
"In this case it was particularly crucial that the children should remain at their school and receive the stability they needed through a difficult time."
David Murray, chief executive of forces charity SSAFA, said: "It is a great shame that a military family must put themselves through a complaint process, simply to avoid disadvantage."
The council said: "We got this wrong and we've apologised to the family and made financial redress.
"We have a duty to spend public money wisely but, as the ombudsman recognises, we have already reminded our staff of the requirements of the Armed Forces Covenant so this situation doesn't happen again."
A council has been criticised for the way it treated a military family whose son had cancer.