Hi Elizabeth
I think this is about Nova Scotia, so I'd like to help. But your post is a bit hard to follow -- what connection are you seeking exactly? Who is the Mary Canon you refer to? You may get more traction if you could add more details, locations, and sources to your profiles.
Are these 2 Thomas Miller profiles meant to be the same person? (They are both currently indicated to be married to the same woman.) If so, they should be merged.
https://www.wikitree.com/wiki/Miller-74651
https://www.wikitree.com/wiki/Miller-23757
The marriage record linked in the profile of Elizabeth (Miller) Alderdice (abt. 1850 - 1912) indicates that her father's name was Robert, not Thomas.
Okay fair enough. This place and time are not my expertise so I probably can't be of any help. But since this marriage record ( https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1873/11283/8139454.pdf ) for William Alderice and Elizabeth Miller says otherwise, I would suggest adding some research notes or sources that demonstrate Elizabeth's father was named Thomas.