I don't know if this is helpful, but the Notts FHS CD has no baptisms for Stoke Bardulph, but there is a transcription from 1836 thus:
18 Sept 1836 Mary PARKER father James (labourer), mother Jane, abode Stoke, bapt at Gedling All Hallows
Gedling is only 2 miles from Stoke Bardulph.
I think "Parker" is a mistake either on the PR or on the transcription as here are some other baptisms at Gedling, some of which are probably the same family, note the varying surname
1826 08 20 William James PARKS Alice Labourer Stoke GEDLING All Hallows
1828 12 29 Elizabeth James PARKS Alice Labourer Stoke GEDLING All Hallows
1830 02 05 George James PARKS Jane Labourer Stoke GEDLING All Hallows
1831 11 20 Martha James PARKS Jane Labourer Stoke GEDLING All Hallows
1833 10 29 James James PARKES Jane Labourer Stoke GEDLING All Hallows
1836 09 18 Mary James PARKER Jane Labourer Stoke GEDLING All Hallows
1838 05 05 William James PARKES Ann Labourer Stoke GEDLING All Hallows
1839 05 12 Jane James PARKS Jane Labourer Stoke GEDLING All Hallows
1841 11 14 Rebecca James PARKES Rebecca Labourer Stoke GEDLING All Hallows
1845 06 08 Rebecca James PARKES Anne Labourer Stoke GEDLING All Hallows
I'm confused about how many James there may have been when you look at the mother's names for these children. The only marriage I can find at Gedling that might fit any of these is this one:
1837 09 13 James PARKES Ann LACEY GEDLING All Hallows
I can't see any marriages for a James Park% to a Jane, Alice or Rebecca!!
I see in 1841, 4 year old Mary Parkes is in Stoke Bardolph with Jane (age 40, charwoman) and 4 other children who match some of those above.
There are a large number of Parkes/Parks burials at Gedling which state that the person lived at Stoke; these include:
1853 06 08 James PARKS 64 Stoke
1890 11 21 James PARKES 76 Stoke
I'd guess one of these would be Jane's husband.
This is probably Jane's burial:
1865 04 06 Jane PARKS 75 Stoke Gedling - so yob around 1790, so I suppose the older of those two James (died 1853) is probably more likely to have been her spouse.