Hi Buffa,
There is a death on Scotlands People which could be for daughter Elizabeth.
Elizabeth Leaper year of death 1968 - Dumfries Dumfriesshire year of birth 1890.
She could be married and have a married name - the search engine will throw up maiden names in the surname box as well as married names.
This death could perhaps give you her parents names (including a married name for her mother IF she ever married
). Only drawback is that you would not be able to view this cert. online as 50 years need to pass before death certs are available to view. You would need to order a copy of the cert which would cost more.
When I suggested Joseph had been mistaken when stating mother Elizabeth was dead in 1916 - I meant that perhaps he did believe she was dead (perhaps had lost contact with her many years ago). A long shot to consider - but stranger things have happened. She wouldn't be the first deceased parent on a marriage/death cert etc to have been discovered still alive on the next Census return.
Both Elizabeths could as Ev has suggested moved abroad. Or even just south of the border. Living in Dumfries it would not take a lot of effort to travel over to England.
Good luck with your hunt,
Looby