I don't think you have gone wrong at all. The person who was the informant for Harriet's death probably did not know her mother. Death certificates often have wrong information.
The record I looked at is an image of the church register and her mother's name is definitely shown as "Celia".
FreeBMD has a death in the March quarter, 1840 for a
Cecilia CROSS, registered at Kingsbridge, Vol 9, p 239.
The church records show Cecilia CROSS, 57, buried Dodsbrooke, 5 January 1840
There is a record (also Dodsbrooke church) of this marriage
John CROSS, sojourner, and Coelia SMITH, spinster, both resident Dodsbrooke,
Marriage date 17 Jun 1806
John signs his name, Celia marks a cross
Witnesses: Simon SMITH, William SINKINS, Elizabeth THORNING
Another sibling for Harriet
John, baptised 17 Nov 1808
(Elizabeth THORNING's baby is baptised earlier that year)
Judith