Thank-you for your quick responses. I will try to fill in some details. My connection is through William Barker, Jemima's husband. All we know about Jemima's family came from a couple entries in William's diary written in 1879. He listed five family members that died in a short period of time. I had assumed the listing was chronological and were in this order Mother's father, Father's father, Father's sister(d 1864), Mother's mother(d 1865) and then Mother(d 1867). The last three we know the dates and they are in order. From the clue Mother's mother dying, a family member found the death certificate and found her Mother's mother was Hannah Parker, dying Sept 15, 1865 in East Halton witnessed by a Barker family member. Death certificate said 79 years old, I believe the age 89 in the parish records that Geoff-E found, mentioned above, is off by a decade. Death certificate said her husband was Thomas Parker. That will match with the census of 1861 giving approximate date and location of birth of Thomas and Hannah both in the mid 1780's, and Thomas in Irby- Lincolnshire, Hannah in Skeffling Yorkshire . The other clue in the diary was Mother's father died previous to Hannah and had been living in Humberstone. Census of 1841 and 1851, and 1861 seemed to show they lived there a number of years. Mother's father,Thomas Parker, died in Humberstone in April of 1863, parish records provided by Geoff-E, mentioned above. We do have father's father , Thomas Barker's death certificate, showing he died July 31, 1861, in Caistor in the Caistor Union Workhouse. So I guess William had the deaths of the two fathers in the wrong order. I also see in the diary that he mentions mother's mother, Hannah Parker, living with them two years before she died which would match well if her husband Thomas Parker died in 1863 and she died in 1865. Hope this will make sense.
I recently confirmed a connection with Mary Ann Parker Mitchell(b 1821) living in the United States Mercer County Ohio married to Thomas Mitchell to be Jemima's sister which was new news. The question still is did Jemima and Mary Ann have any siblings. No idea of Hannah Parker's maiden name either. Thanks