Hello Liz,

Sorry to hear about your poor head!

You've missed the messages I posted on the earlier (separate) section of this thread on 7th Jan., which were mainly from the Cheshire FHS records of b/m/d.
According to this, the Michael who died in 1864 was aged 2:
CAIN, Michael, 2, Runcorn, Halton, RUN/16/15

His birth probably:
Cheshire Birth indexes for the years: 1862.
Surname, Forename(s), Sub-District Registers At, Reference:
CAIN, Michael, Runcorn, Halton, RUN/23/35

I think father Michael's death was:
Cheshire Death indexes for the years: 1866.
Surname, Forename(s), Age, Sub-District, Registers At, Reference:
CAIN, Michael, 34, Runcorn, Halton, RUN/17/63

I also found a marriage on the IGI (extracted entry): Michael Cain (father John Cain) and Margaret O'Neil (father Michael O'Neil) on 7 Sept.1863 in Warrington, Lancashire.

Cheshire Birth indexes for the years: 1864.
Surname, Forename(s), Sub-District, Registers At, Reference:
CAIN, Bernard, Runcorn, Halton, RUN/26/29

See: www.cheshirebmd.org.uk for a guide to order any of these. It used to be cheaper to order from the local RO.
I agree with Averil that this is the most important one to get (Bernard birth 1864), along with his son USA Bernard (to find out where the family was).

This could be John O'Day's stepdaughter Mary Kane aged 5 in 1871 census:
1866:
CAIN, Mary Ann, Runcorn, Halton, RUN/29/11

Re. your message, where you have "margaret kane ireland wife age 48" that is what Ancestry put in the index, but if you look carefully at the scan I think it has been crossed out and "40" written above (but I could be wrong).
Yes, I think Margaret (possibly O'Neil) married Michael Cain who d.1866, and then John O'Day in 1867. Possible children were:
Cheshire Birth indexes for the years: 1867
Surname, Forename(s), Sub-District Registers At, Reference:
O'DAY Bridget Widnes Halton WID/15/31
1869:
O'DAY Catherine Widnes Halton WID/17/57

Michael Cain and Margaret's children included Michael 1862-64, Bernard b.1864, and Mary Ann b.1866.

The Bernard Cain aged 17 in the 1911 census (which was signed as correct by Bridget Cain - so she wrote that her son was born in New York) was Catherine Cain's brother, and the son of Bernard Cain & Bridget Doherty.

I can't remember where I got the birth ref. from: Bernard Cain Liverpool 1895 Vol 8b, Pg 35, so it needs double-checking in case there are other possibilities.

Sue