Hi,
Welcome to RootsChat

I can see the image of their marriage at FindMyPast, but the marriage was in Yorkshire,
28 Dec 1835
Cathedral Church of St Peter & St Paul, Sheffield
Joseph BARKER of this Parish, Bachelor a
and
Henrietta FOSBERY of this parish, Widow
were married in this church by Banns.
Joseph made his mark, Henrietta signed.
Witnesses: Elizabeth COTTON (her mark), Joseph HUDSON
In 1841 they have Emma age 4 living with them but I think she was born before the beginning of birth registration in July 1837. By 1851 Henrietta has two more children Benjamin 10 and Fanny 16 living with her, I think these are their births as shown on the GRO site,
https://www.gro.gov.uk/gro/content/Benjamin BARKER Jun Q 1840 Worksop Union 15 649
mmn: KILLOUFF
Fanny BARKER Jun Q 1844 Worksop 15 670
mmn: -
It looks possible that Henrietta might have been born a KILLDUFF who then married a FOSBERY and when he died she married Joseph BARKER.
Regards,
Daisy