Hi, Trish & Sue -
The reason Joseph James wasn't Ernest's next of kin is that he died in 1909.

The assumption that Joseph James was still in England in 1883 is not proven. The death of his little boy could have happened in Deal no matter where Joseph was. But I believe he and Wallace did go out to Australia together - they did everything else more or less together! - and Wallace was still fathering children in late 1882.
But I HAVE just made a breakthrough!
All previous searches for JJ's family post-1883 I did using Hannah's name and birthyear, birth place etc - and failed to find anything, even using just her first name. I should have tried spelling it wrong!
Because just now I tried it using just Agnes's first name and details. And lo and behold, there they are - Hanah, Joseph and Agnes. In Herne Bay in 1891, living with Lewis Edward Golder as his wife and children:
Lewis Edward Golder 34
Hanah Golder 38
Joseph Golder 14
Agnes Golder 10
Jessie Golder 8
Ellen Golder 4
Jessie Cornhill was born qe Mar 1883 in Eastry.
Ellen Amelia Cornhill was born qe Mar 1887 in Medway.
There is no marriage for Lewis/Louis Edward Golder to a Hannah of any description.
I would suspect that the original assumption is probably correct - Jessie was probably the daughter of Joseph James, born in Eastry which covers Deal, where she and JJ had been living. Which means JJ could not have left UK before mid-1882. Then there's a four year gap before Hannah has the next child, who is probably that of Lewis Golder, born in Medway which is quite a way up-county from Deal.
So what happened? Did JJ and Wallace go off to Australia promising to send for the family? Or did they just scarper? Transportation was over by then, so that can't be the answer.
Clearly JJ didn't die in UK - not only is there no record for him, but also surely Hannah would have married Lewis Golder if JJ was dead?
So the balance of probability now is that JJ and Wallace left England some time in 1883 or 1884 bound for Australia. Wallace doesn't appear to have remarried - and died in 1902. There is no info on his listing in the death index, so whoever registered his death knew little about him. JJ struck up a relationship with Ada Mary Rope before 1886 and had two children with her before finally marrying her in 1891. However, he did so bigamously, because his English wife was still alive and kicking in Herne Bay in 1901....
That COULD be the answer to the late marriage to Ada though - by then she was living as Hannah Golder, and he may have tried to trace her and failed, so presumed she was dead?
Yet another skeleton to add to my Cornhills - JJ's grandad appears to have abandoned two daughters in Berkshire as well!
PS Just seen the post from Cazay - thanks for looking! Anything you find would be most welcome...!