From info from baptism, I think the marriage of Hannah Price to Robert Smith on 30 Dec 1839 Wrexham are possibly correct parents for Jane. (Marriage image online)
Likely death of Hannah, death cert would confirm
Name Hannah Smith
Death Age 26
Record Type Burial
Birth Date 1819
Death Date abt 1845
Burial Date 6 Mar 1845
Burial Place Wrexham, Denbighshire, Wales
Page number 59
Robert then marries spinster Mary Dodd in 1846 (image online) who names her father as William Dodd. I believe Thomas Dodd (father William) who married Mary Roberts (image online) was brother to Mary Dodd the 2nd wife of Robert Smith. Which would make him uncle by marriage to Jane Smith
Thomas & Mary Dodd were likely childless so likely the Dodd family took Hannah Jane, as in 1881/1891 census and helped raise her.
Unfortunately 1841 for area seems sparse or missing?. The 1851 for Dodd family born Moss is there.
There may also be a sister for Jane, that is working as a servant in 1851. (With possible Aunt nee Price)
https://www.ancestry.co.uk/search/collections/8861/records/16107841Name Eliza Smith
Baptism Age 0
Record Type Baptism
Birth Date 1840
Baptism Date 27 Nov 1840
Baptism Place Brymbo, Denbighshire, Wales (image is Broughton)
Father Robert Smith
Mother Hannah Smith
Page number 15
Just my thoughts
Cas