I think the 1889 death could be correct and then Robert (given he had a young family) remarried:
Possibly:
4089/1891 / INGLETON ROBERT / SMITH MARGARET / GOULBURN
So she would be the Mrs Robert Ingleton and widow referred to in the newspapers...
Her death notice seems to confirm:
http://trove.nla.gov.au/ndp/del/cite/1111823/17230250Burial at Woronora...with Robert
http://www.woronoracemetery.org.au/finding-loved-onesMatches this death reg:
22622/1935 INGLETON MARGARET / JOHN / 83 YRS CRONULLA / SUTHERLAND
Mary's death in Leichardt matches the birth reg district of youngest child:
14335/1880 INGLETON JOHN / ROBERT / MARY LAIRD / GOULBURN
9898/1881 INGLETON JEANNETT / ROBERT / MARY L / GOULBURN
4992/1886 INGLETON ROBERT / ROBERT / MARY L / LEICHHARDT
Baby Robert's death:
5831/1887 INGLETON ROBERT / ROBERT / MARY / GOULBURN
This could be the death of Jack (son John?)
21071/1958 INGLETON JACK / ROBERT / MARGARET / ROCKDALE
Possibly his marriage, and wife's birth and death
13538/1914 INGLETON JOHN / MACREADY ISABELLA A / SYDNEY
6764/1883 MACREADY ISABELLA A / HUGH / MARY / NEWTOWN
28603/1967 INGLETON ISABELLE AGNES / HUGH / MARGARET / KOGARAH
Isabella's mother's maiden name was McARTHUR. These are likely to be WWII enlistments of two sons of theirs:
INGLETON ROBERT MCARTHUR : Service Number - NX8270 : Date of birth - 22 Dec 1919 : Place of birth - ROCKDALE NSW : Place of enlistment - PADDINGTON NSW : Next of Kin - INGLETON JOHN
INGLETON COLIN MCARTHUR : Service Number - NX57056 : Date of birth - 08 Jan 1920* : Place of birth - ROCKDALE NSW : Place of enlistment - PADDINGTON NSW : Next of Kin - INGLETON JOHN
*I think this should be 1922!
Both married (see link below); both died in 1972, see
http://ryersonindex.net/search.phpBDMs from
http://www.bdm.nsw.gov.au/bdm_fh.html