Part of the A684 will close from 26 October in the final part of the Sedbergh roadworks project.
Westmorland and Furness Council found a historic mapping system error had caused the mix up.
It will cost Sam Shuttleworth about £3,400 a year if her children stay at the Kirkby Stephen school.
Westmorland and Furness Way is a continuous route through Cumbria from Alston to Furness Abbey.
The works, running from 14 September to 16 October, form part of a scheme improving the A684.
Westmorland and Furness Council says it will try to keep disruptions to a minimum.
Diversions are in place for the closure between 09:30 and 14:30 GMT for five days from 16 March.
A coroner says the road should be reviewed after the deaths of two women in a bus and car crash.
The death is not being treated as suspicious, Cumbria Police says.
