I wonder if this is the birth of Ethel M SWAN -
NSW BDM birth
10056/1880 SWAN Ethel May parents John /Eliza @ Bathurst
The birth certificate for Jack SWAN, 1900, will show age and birthplace of mother Ethel, which should assist in identifying her SWAN family.
If Ethel SWAN is having a family with John REYNOLDS, and there is no marriage to find, the most likely reason would be that Ethel SWAN and / or John REYNOLDS are still married to someone else.
We have reason to believe that Ethel M(ay) is alive at 1922. Ethel might be using a name other than SWAN or REYNOLDS, depending on her domestic arrangements after the 1911 departure of John Thomas REYNOLDS, which absence is suggested by the children-in-care records.
Using NSW BDM...deaths.....Ethel M........parents John / Eliza....died 1922 +....in an inner (Sydney) city location has several possibilities but I am not getting anywhere with this.
By the social conventions of the times, Ethel, in old age, would most likely go to live with an adult daughter.
Burial places of daughters Heba/Eva WILSON and Victoria WARR would be useful as they might also be burial place of mother Ethel M(ay).