Goodness Jocelyn you've come up with such a lot in a short space of time... it took me much longer to find the bits and pieces I know!!
I'd come across the article about the murder trial-I do love trove-so was aware of the possibility that Cornelius might have been going under the name of Neal/Neil/Neale/others? He abandoned LydHen just after the trial & I wondered whether he was implicated in some way with respect to the murder but the newspaper article doesn't suggest that. The article also says he was living in Prahan, he had an aunt who lived there, so perhaps that is where he & Lydia were staying. LydHen's State Ward papers say her father Cornelius was thought to have gone to Sydney (from Melbourne). He may have left LydHen in the care of his aunt MaryAnn Brace but she was sick & died in early 1871, so it may have been the aunt who was unable to care for her.
I'm working on the Chidgeys with a lady in NZ who has a lot more info that I have on the Chidgey ancestors, I'll pass your other info to her.
You're right about the Lydia who married Mr Cox. She was Cornelius's younger sister.
Cornelius's parents & siblings settled in NZ. I've seen the death certs of both parents. Cornelius is recorded as alive in abt 1894 when his mother died & dead in 1909 when his father died. However, I'm thinking he may not have been in contact with his family after he left NZ in 1868/69, so recorded on his mother death cert as alive because his siblings hoped he was but dead on his father's death cert because he was the oldest male & settling the will may have been hard if they claimed he was alive but had no knowledge of his whereabouts. I haven't had any luck finding a copy of the will.
Thanks for your efforts