Hi - There is a gap between these two children who appear under both parents' surnames:
Margaret John Corkill/ Margaret Kermode Parish Church 1 Oct 1848
William Henry John Corkill/ Margaret Kermode Parish Church 23 Apr 1854

These children were bapt without mother Margaret's surname:
CORKILL John John Corkill/ Margaret Parish Church 15 Sep 1850
CORKILL Edward John Corkill/ Margaret Parish Church 20 Jul 1851
CORKILL John John Corkill/ Margaret Parish Church 16 Nov 1851

There were also a John Corkill and Margaret Corlett having babies bapt around the same time. Edward and the second John's bapts are too close together to have the same mother (unless one was a late bapt). Censuses usually sort out these families.

John C & Margaret Kermode's son John was aged 6 months in the 1851 March 30/31 census, so if accurate that would make his birth date Sept 1850.

Don't some US censuses give birth dates? Could you please post these for father John as well as for his children?

You wrote "There is also another Corkill that seems to have been with John when he first appears on the US census in Galva, Illinois. A William just 2 years older though".

Can you please be more precise?

Date of census? Could you also write out the full details given in this census for all the Corkills?

Sue