The distance calculated by North Yorkshire Council is based on a road entrance to Tadcaster Grammar, but Ruth, who is a GP, discovered a pedestrian gate which made it the closest school by 27 metres.
However, she said officials stated that the school "had not informed the council of this gate being put in more than five years ago".
"When they applied the policy, the gate - in their knowledge - didn't exist, so despite the gate being present, it doesn't matter, you lose your appeal."
She said the authority planned to update its mapping software, but in the meantime, she has had to pay for a bus pass for Henry.
"That failure in communication apparently is not their fault and I have to bear the brunt of that as a parent, which is £818 this year."
Her stage two appeal was unsuccessful, with the authority saying it did not accept that parents were unaware of the policy when applying for school places.
She added: "Yet it's OK for them to have not communicated with the school around a gate.
"It seems like it's one rule for one and one rule for another."
She said during the appeal, it felt like the five councillors hearing the case saw it as a "done deal".
"This is days of effort that have gone into unpicking, investigating and putting forward my case.
"For them only to ask one or two questions in the appeal process feels like they didn't really want to unpick my case."