This is a frustrating one, isn't it! Her children would surely have known that she was indeed deceased by the time they were married, so the window really should only be from 1921 to 1931. It does seem strange that the informant on Charles Milne's death is his sister-in-law, especially as he died in hospital, but might explain why Jessie is given as Jessie Maitland, rather than Leith.*
*Edited to add - Jessie would have been Maitland, as her mother later married her father!
However, if something happened between 1921 and 1931, as Charles and Jessie don't seem to be living together, then it may be that the children lost touch with their mother and assumed that she had died. Widening the date range at at Scotland's People centre might be an idea, as you'll be able to view more certificates that way, including those beyond the cut off dates.
Could she have gone to prison? Newspapers might have something, it'd be worth a look if you've not done so.
What's also frustrating is that the Aberdeen city poor records for that time are very patchy, with no real records surviving. There is a list at the city archives (archives [at] aberdeencity.gov.uk) of people who were in Oldmill and in receipt of poor relief under reference C/16/3/1. They are currently closed as they're moving premises, but it's worth an email to them. There are also Woodend Hospital records held at NHS Grampian Archives (gram.archives [at] nhs.scot) - they might not give you any more information than is on Charles's death cert, but again worth an enquiry.