Just thinking dates here and working from the bits of info you have mentioned:
1895: Birth of Michael Conroy Snr. You have all his details up to 1911.
1907-8: Possible birth year of Elizabeth McDonell (with all its variants!) given the DC found in 1934 for a Mrs Elizabeth Conroy, aged 26 at the time of the death.
1911: Michael Conroy still shows on the Scottish 1911 census.
1914-18:
Why does the family think he changed his name/age to enlist?1928: Mary Conroy born 12th September 1928 in Youghal, Co. Cork (although no BC found yet to confirm), died in Scotland in 2003...
aged 74-5? You mentioned that Mary had struggled to find her BC at the Registrars at Youghal in later years.
1930: Michael Conroy Jnr bornborn on 20th July 1930 in a workhouse in Newry, Co Down, NI. Parents were Michael Conroy and Elizabeth McDonnell.
1928-34/5: Possible younger siblings to Mary, Patrick and Annie died, maybe at the same time.
1934: A Mrs Elizabeth Conroy died aged 26 on Thursday, 12th July 1934 in Belfast area. You have found a DC, which gives her death from TB and husband a Michael Conroy, a labourer.
1934-5: Young Mary goes to Glasgow area to live with family.
Was she the only living child from the family?1962: Death of Michael Conroy (b. 1895 Glasgow) so aged c. 67? Elizabeth McDonald showing as his deceased wife.
From this, Michael Snr never remarried? When did he come back to the Scotland (he must have done given his wife's name was included on his DC).You know me, I like timelines
Not sure it helps given the lack of records so far, but it would all fit in terms of dates wouldn't it?
Monica