John Tinker married Catherine Pettefar 13 April 1836 in Kirkburton. They were both aged 23 and gave their residence as Newmill, Yorks. According to the 1851 Census Catherine was from Nwark, Notts.
I have found 4 children Elizabeth registered 1840 Huddersfield
Ellen 1839 Huddersfield
Eliza 1840 Newark
Edward 1842 Newark. All have mmn Pettefar
FreeReg has the baptism in Newark, Notts of Edward, Eliza and Ellen inMarch 1842. All three baptisms give John Tinker's occupation as Innkeeper so I'd say Publican is correct in the 1841 Census.
Emeltom