Monaro Pioneers site has some information re Patrick BARRETT who married Elizabeth GRIGGS. this site is usually reliable but you would need to check for yourself. I think you may have to register to view it but it's free.
http://www.monaropioneers.com/TNG/getperson.php?personID=I228268&tree=MPPatrick BARRETT, b 1864
Parents:
Patrick BARRETT, b. 1821, County Limerick, d. 18 May 1918, Reidsdale, NSW (Age 97 years)
Ellen COMANS, b. 1835, Balintemple, d. 1 Jun 1909, Braidwood, NSW (Age 74 years)
the date of this couple's marriage (your Patrick's parents) is:
11 Sep 1853 Catholic Church, Araluen, NSW,
Ref: NSW BDM Index, V1853510 99/1853
Elizabeth GRIGGS, 10 Jun 1862, reg Braidwood, NSW BDM, 6022/1863
Her parents:
James GRIGGS b. Abt 1801, Surrey, England,d. 4 Jan 1884, Braidwood,
Harriett VIDLER, b. 24 Oct 1830, Sandhurst, Kent, d. 19 Jan 1914, Braidwood, New South Wales
Married: 9 Apr 1851, reg Narellan, NSW BDM Index, V1851372 37B/1851
The children listed for Patrick and Elizabeth are the three you mention earlier -
William John, b. 1888, Braidwood, d. 10 Sep 1955, North Sydney,
Annie Margaret, b. 1891, Braidwood,
Patrick b 1894, Braidwood
It is useful to remember, unless the actual place of birth is specified, the place referred to in indexes is usually the place of registration, which in country areas may be some distance from the birthplace.
Monaro Pioneers lists siblings and parents for your Patrick and for Elizabeth.
Also the arrival of
Ellen COMANS per ship
Calcutta, aged 3, her parents.
Judith