Thank you everyone for your interest and help. It's certainly not butting in, but helping a poor gentleman (?) in distress!!
Thank you
Dizzy for that newspaper reference, I certainly hadn't seen that before and I had searched a good newspaper site. That is certainly my grandfather and his second wife. There are some interesting and curious things about this report. (1) A Gertrude M Hargraves, who I presume is the same person, died in 1934. I don't have the date, but as this court case was in November, it must have been soon afterwards. (2) I may try to look up the court documents, as they may (just possibly) say something about how long Ernest had been in Australia. (3) Ernest was familiar with the inside of a court room. He had been there to finalise his divorce from my grandmother (1922/23), and (according to my mother's recollection) he had been taken to court several times by my grandmother to pay maintenance for his two daughters. Now this. (4) That Trove site is not one I can recall seeing before, but it looks helpful. So thanks for all that.
Mary, I had found the death notice on another newspaper site, but thanks for letting me know. I too had found Francis & Mary at Hebden, not only in 1881, but also earlier. Ernest was supposedly born in Lincoln UK, but one person (I think it as Tony on this forum) suggested that it could have been Linton UK, written down incorrectly. Linton is a town next to Hebden in Yorkshire, and the parish is named Linton. So that seems a good hypothesis to start with. But it runs into problems ..... (1) I can find no mention of Ernest's birth (about 1880/81) nor any mention in the 1881 or 1891 census of him or any other children living with them. They would have both been a few years either side of 40 by the time Ernest was born, so you'd think there's be other children. (2) He (according to the time he'd been in Australia recorded on his marriage certificate) migrated in about 1899, but he's not anywhere else I can find in the 1891 census, nor on any shipping list. (We did find some plausible shipping notices and a death for Mary Hargrave in Victoria, but they all turned out to be dead ends.) (3) There are a couple of other Francis & Mary Hargraves in northern England, so that makes the Hebden couple less certain
I'm inclined to think the ones you mention are the correct ones, and they simply didn't have children until late or the children weren't included in the census for some strange reason, but the fact that I can't find a plausible Ernest anywhere in England is disconcerting. With no birth, no census, no shipping, it makes you wonder whether something is wrong, and he came from elsewhere, or changed his name or something. If you have any information that throws light on any of this it will be very gratefully received! Thanks.
JAL, thanks again for your continued helpfulness and cheerfulness. Let us hope you are rewarded with a find!! Thanks.
If only our ancestors knew what stress they give us trying to trace out their unlikely lives, they would have made things clearer! or perhaps not!!
Even better to hear that you are making some progress with your elusive grandmother thanks to the eagle eye of a relative. Good luck with chasing up the adoption and keep in touch. 
but we all keep at it intermitantly 
In FH the more force against brick walls the better 