This is likely why Kate was admitted to the Destitute Asylum.
South Australia Birth Index. (Genealogy SA,
https://www.genealogysa.org.au/index.php : accessed 27 September 2021) birth transcript for MCAVANEY, Myrtle Mary (Gender: F, Birth Date: 17 March 1910, Father: , Mother: Katie MCAVANEY, Place of Birth: Adelaide) Reference: District: Adelaide, Book/Page: 838/259.
The Annie McAvaney at Peterborough was formerly Annie Crittenden.
South Australia Marriages 1842-1937 (FindMyPast,
https://www.findmypast.com ; accessed 27 September 2021) transcript for McAvaney, Patrick (Age: 30, Status: Single, Father: John McAvaney) and Crittendon, Annie Jane (Age: 28, Status: Single, Father: John Crittendon) on 11 November 1884 at [Unrecorded] Kapunda, Reference: District: Kapunda, Book/Page: 141/705.
Their children appear to be born in and near Kapunda and if you search Trove you will see that both Annie and Patrick had a long history of trouble with the law. Annie was in Peterborough after 1900, as was her mother Sarah Crittenden.
South Australia Deaths 1842-1972 (FindMyPast,
https://www.findmypast.com : accessed 27 September 2021) transcript for McAveney, Patrick (Death Date: 8 July 1912, Marital Status: Married, Age: 58y, Residence: Caltowie, Death Place: Caltowie) Reference: District: Clare, Book/Page: 367/35.
South Australia Deaths 1842-1972 (FindMyPast,
https://www.findmypast.com : accessed 27 September 2021) transcript for McAvaney, Annie Jane (Death Date: 13 February 1919, Marital Status: Widowed, Age: 64y, Relative: Patrick Mcavaney (Deceased husband), Residence: Peterborough, Death Place: Jamestown) Reference: District: Clare, Book/Page: 425/487.
There are only 3 children registered for Annie and Patrick, so you're in for some fun.
South Australia Birth Index. (Genealogy SA,
https://www.genealogysa.org.au/index.php : accessed 27 September 2021) birth transcript for MCAVANEY, Ellen (Gender: F, Birth Date: 3 March 1888, Father: Patrick MCAVANEY, Mother: Anna CRITTENDEN, Place of Birth: Nr Kapunda) Reference: District: Kapunda, Book/Page: 415/190.
South Australia Birth Index. (Genealogy SA,
https://www.genealogysa.org.au/index.php : accessed 27 September 2021) birth transcript for MCAVANEY, Fanny Eliza (Gender: F, Birth Date: 16 July 1885, Father: Patrick MCAVANEY, Mother: Annie Jane CRITTENDEN, Place of Birth: Kapunda) Reference: District: Kapunda, Book/Page: 356/188.
South Australia Birth Index. (Genealogy SA,
https://www.genealogysa.org.au/index.php : accessed 27 September 2021) birth transcript for MCAVANEY, Edward (Gender: M, Birth Date: 15 October 1891, Father: Patrick MCAVANEY, Mother: Annie CRITTENDEN, Place of Birth: Kapunda) Reference: District: Kapunda, Book/Page: 490/307.
In 1893 two of Annie's children, Ellen and Edward, were removed due to neglect and sent to Magill. Once the kids are in the system there are usually very good records of them, at State Records.
https://trove.nla.gov.au/newspaper/article/108449587?searchTerm=%22annie%20mcavaney%22
In January 1884, Patrick McAvaney was charged on information supplied by Anne Crittenden, for neglecting to maintain his 2 illegitimate children. They're not registered.
https://trove.nla.gov.au/newspaper/article/106577018?searchTerm=%22patrick%20mcavaney%22
In January 1890 Patrick was charged for failing to support his 3 children, and at this time we know he has 2 children born since his marriage, plus 2 prior to marriage.
https://trove.nla.gov.au/newspaper/article/108351269?searchTerm=%22patrick%20mcavaney%22
South Australia Deaths 1842-1972 (FindMyPast,
https://www.findmypast.com : accessed 27 September 2021) transcript for McAvaney, Annie Jane (Death Date: 13 February 1919, Marital Status: Widowed, Age: 64y, Relative: Patrick Mcavaney (Deceased husband), Residence: Peterborough, Death Place: Jamestown) Reference: District: Clare, Book/Page: 425/487.
