I think this is only very complicated on whatever odd website your using; and maybe just inside your head.

Your flying YYT-YYZ-LHR and DUB-LHR-YYZ-YYT; regardless of what the contracted booking shows you are confirmed on those flights; will fly them in that order on those dates.

Why do you think you will need to check in multiple times and check lugage multiple times; your ticket is just that a ticket that has all those flights on it.

Instead of using some website why not look up the booking on the aircanada website; you will most likely toward the bottom notice there are 2 ticket numbers 014xxxxxx; one for the YYT-LHR and one for the DUB-YYT