Hi Doug,
Barton, although in Yorkshire is very close to the border of Co. Durham.
This one appears to be a close possibility, see what you think .. ..
1841 census:
HO107/304/1, folio 5, page 4
Durham, Denton
Thomas Davison senr. 65, Blacksmith, Y
James senr. 30, Blacksmith, Y
Elizabeth, 30, N
Thomas jnr. 6, Y
Richard, 6, Y
James jnr. 5, Y
John, 3, Y
William, 2 mths. Y
/
Ann Wade, 11, N
//
It looks as though Ann has not been included in the family unit.
Denton is 6 miles away from Barton and Ann is listed as not being born in county.
Kind regards,
Pels