Is it possible that Reynolds was not her birth name? There is one Sarah with a possible match born 6 September 1912 in Castlederg, surname Mulligan, father's name William, and mother's name Margaret Ann Sproule from Altamullin.
Many thanks to you, didn't realise at the time how valuable your reply was.
Two years after I originally posted this 'mystery' as user cogs291 I have found through DNA that you hit the nail on the head with your theory of Reynolds not being my Mothers birth name, and that she was the Sarah Mulligan you suggested.
I've since been able to research her Milligan/Mulligan family from Altamullan and connect with some cousins around the world - though many of her siblings descendants remain elusive after the family split, as does the reason she used the Reynolds name for her wedding.
So the full mystery for me remains to be solved, but I've learned not to dismiss suggestions like yours so quickly and not to trust paper records.