Jezza
I assume the ones from Bradfield are not yours - there were other children with these prents but they could be another Joseph and Hannah.
If Joseph and Hannah married in Yorkshire, here is one potential marriage - not necessarily them, but a possibility. Not sure of the geography of Yorkshire and how far away this is from Barmby.
Joseph Kay and Hannah Wilson 30 Nov 1814
Thornton by Pockington, Yorkshire
This date would also fit well with Grace's birth....
If they married outside of Yorkshire, there are LOADS of Joseph Kays who married a Hannah!!!
Interestingly, there is also a marriage at the same place for the following
Margaret Kay and John Wilson 3 Jul 1814
Thornton by Pocklington, Yorkshire
Regards,
Claudia