I am pretty sure that I have got the correct parent from my research (below) but I can't find a baptism for my 4x great-grandmother.
The first record I have for her is her daughter's, Dorothy Barbara Parkinson, baptism in 1832 in Cambridgeshire, where she's called 'Hannah', with 'husband' William Parkinson. They're 'of no fixed abode'. They then have Mary Jane Parkinson in Ripon (according to all her later censuses, other than one which says she was born in Nottinghamshire) in 1835. Their third child, Henrietta Ann Parkinson was born in Lancashire in 1837 (before July). Their fourth child, Frederetta Ellen Parkinson, was born in 1839, and on the birth cert Hannah is called 'Hannah Parkinson, formerly Hunter'. Their last child, Nancy Ruth Parkinson was born in 1841 and on there it says 'Ann Parkinson, formerly Whitehead'.
On all them births their father is William Parkinson who I think is actually Hannah's uncle. On the 1841 census, in Lancashire, neither are born in Lancashire, William was born 1796 and Ann was born 1811. The woman who I'm pretty certain is her mum, Dorothy Parkinson, who married a Richard Hunter in 1813, had a brother called William born in 1798 and on his childrens' burial records (in 1817 & 1820) and also his wife's second marriage (in 1826) his wife is listed as a widow, but I can find no death for a William Parkinson.
By October 1841 Hannah is back in Ripon, marrying Mark Kirby. They married by licence and she's a spinster with her father listed as William Whitehead, wheelwright.
Henrietta and Nancy Parkinson both die in 1842 in Leeds and they're both buried as the 'child of Mark & Ann Kirby. They have two children, Mark William Parkinson Kirby, born in Leeds in 1843 & John Thomas Kirby, born in 1844 in Weeton.
Mark Kirby (the elder) died in a railway accident in Harrogate in 1846.
Dorothy Barbara Parkinson dies in Ripon in 1849 and is buried as a Kirby, daughter of Ann Kirby, widow.
All the children who survived to marry so far have named their father a Mark Kirby (John Thomas named him John Parkinson Kirby for some reason).
The next mention of Ann is in 1848 when her daughter is baptised as Sarah Henrietta Kirby in Ripon with 'Ann Kirby, widow'. Sarah Henrietta wasn't registered until Sept 1848 as Elizabeth Raine with parents Ann Raine, formerly Parkinson. THe next child is Charles Aron Raine Kirby with mother's maiden name Kirby, and he died in 1851 'son of Ann Kirby'. She has three more children, all with the surname Raine, and her maiden name given as Parkinson. On the censuses she's listed as the wife of Aaron Raine and her date of birth varies between 1812 & 1816 and born in Roecliffe/Ripon.
She died in 1869 in Leeds and is listed as 'Ann Kirby, widow of Mark Kirby'. The informant was Jane Mudd, who was formerly Jane Hunter (Mary Jane Raine, Ann's second youngest daughter, married Richard Hunter, Jane's illegitimate son) whose mother was Dorothy Hunter, formerly Parkinson. So, they were [half] sisters.
Sorry for the long and rambling post but I've tried and tried to find definitive proof to back up what I think which is that Hannah Parkinson is the daughter of Dorothy Parkinson.
Any help would be greatly appreciated.