Death/funeral notices from Trove. Given the common Braidwood theme it might be worth pursuing the possibility of the parents being the Patrick/Mary you've looked at.
Peter
Death notice (SMH Sat 25 May): Patrick Barrett. 18 May, 1918, at his residence, Reedsdale, Braidwood, aged 97.
Death notice: (SMH 6 Jan 1919): Patrick Barrett. 4 Jan 1919, at the Mater Misericordiea Hospital, beloved husband of Elizabeth Barrett of Bega, Mitchell Street, St Leonards, aged 60 years, late of Braidwood.
Funeral notice: (SMH 6 Jan 1919): The relatives and friends of Mrs Elizabeth Barrett and family are invited to attend the funeral of her late husband and their father, Patrick; to leave Bega, Mitchell Street St Leonards this day at 10.30 a.m. for Catholic Cemetery, Gore Hill.
Walter Bruce Undertaker, ‘phone North 923, Lane Cove Road, Crow’s Nest.