Just under a year ago I had to return home to another country to look after my terminally ill mother who eventually died... In order to return urgently I had to leave my 14yr old son with his father... simply because I could not afford to pay for his flight... while in his father's care his wife wanted my son out of the house... using emotional, physical & mental abuse toward my son... now my son is in a residential care home in australia while I look after my mother's probate and desperately trying get back to australia... I feel that my son's father did this action on purpose to abandon my son... can I sue him for neglect of his child?
This is just a short summary of what has been happening... please we need to know our rights

Your son wasn't thrown out on the street. You would have to start by proving that the facility didn't meet government standards. You would have to prove that your son was put there for no reason, and find evidence of abuse. You still would probably lose.
He may have been abused, or he may have resented where he was and being left by you(!), or some of both. If your ex resented paying support all those years while you had custody, I would have thought twice about leaving the boy with him.
You chose your mother over your son. I'm not saying that's wrong; it's a Sophie's choice, but you need to see that you are part of this series of events. A year is a long time.

While I don't know the laws in Australia for sure, I can't see any case for suing the father. IF your son was just kicked out of the house with nowhere to go, you could have him charged with criminal abandonment.

You say that now your son is in a care facility, but you don't say how he got there. If the wife did, in fact, abuse him, then family services may have removed him for protection. Again, though this doesn't represent a civil suit, but a criminal case.

The only possibility of a civil suit that I see is if you are getting charged for the residential facility, that might give you grounds to sue the father to recoup those costs.