Do you have any information on the family in Chile? Perhaps we can go at it that way.
Somewhat later on, but this record must surely be somehow connected to your lot:
https://familysearch.org/pal:/MM9.1.1/KZ7D-CRH
This birth record is their grandson. Lydia and George had 2 daughters, one being another Lydia, who married Alejandro Urrutia, and this child in the record is one of their sons. Other than that, the information on George and Lydia is sketchy. George had a brother, Richard, living in Chile and he and Lydia went from NSW to visit him. Another researcher has a copy of a letter written by Richard, (when and to who I don't know) which says, in part:
“
My brother George went to New South Wales some years before me and William to the East Indies.
George used to pay me a visit for years, along with Lidia Aylwin, our cousin, daughter of Gulielmos Aylwin, dealer in copper and both died here a while back.”
Not sure when Richard went to Chile, but he married there in 1836 and died in 1877.
Lydia (the daughter of George and Lydia) was born in Chile in 1844 and died in 1925, aged 81.
The researcher in Chile has so far been unable to find any records for them ... their arrival in Chile, or their marriage, nor how and when they arrived in NSW.