This could be John O'Day's stepdaughter Mary Kane aged 5 in 1871 census:
Cheshire Birth indexes for the years: 1866:
Surname, Forename(s,) Sub-District Registers At, Mother's Maiden Name [not given in index], Reference:
CAIN, Mary Ann, Runcorn, Halton, RUN/29/11

And this could be Michael who died aged 2:
Cheshire Birth indexes for the years: 1862.
Surname, Forename(s), Sub-District Registers At, Reference:
CAIN, Michael, Runcorn, Halton, RUN/23/35

Sue