Perhaps he was buried in a paupers grave and not registered.
Even if it was a pauper's grave he must have been registered as you need that before a burial or cremation, especially as we are talking about the 1900s.
I still think he left the family and perhaps changed his name, so is buried using that name and that is why he can't be found. If he is supposed to have died in 1915 why can't he be found in 1911 and why does she say she is a widow? It just doesn't add up.
Unfortunately re John's birth certificate naming him as father that doesn't mean 100% that he was. If a woman was married, her husband was assumed to be the father, whether he was or not. There have been lots of cases, especially during war time, when men were away fighting at the time the baby was conceived, yet were down as father on the certificate. Could that be why the marriage broke up - she had a baby by another man? I suppose that is where a DNA test would come in handy.