It seems there's quite a lot of speculative material here, that shows the dangers of following what Online trees say, unless you yourself have the proof. That's not, by the way, intended as a rude comment at all, but rather the feeling I've got after reading carefully the pages, and trying to chart it out, and I think that's rather what CaroleW - who I've personally found very accurate and helpful in the past - intended. I hope you don't object to my first sentence here, but that is my impression.
I wish you the best of luck in this search - if Mum has dementia, she may not be able to help you, but there may still be other relatives, with documentation that can help you build up a chart of KNOWN facts, and perhaps agencies such as the Salvation Army may then be able better to work from that starting point?
People with online trees are often reluctant to provide documentation to others - usually because they haven't got it, and often because they have taken information themselves at face value from other trees.
I, and others, have had relatives hijacked, re-spoused and given additional / different children, often whilst having real children "snatched" into oblivion that way.
Online sources are a good guide or help - but don't provide all the answers, sadly. (I too have been chasing a "Jones" marriage for ages!)
Good luck. I'm sure the finest help is that given on here, for free and for interest. I do hope someone can help you to help your Mum.