Air Travel Search EnginesFlight travel search engines
You can find itineraries that combine airfares from different carriers using several different kinds of tools: Air carrier sites usually offer flight deals from other carriers (not only codeshares or allies of the same network, but also flight deals that can be offered through interlining agreements). Of course there are many restrictions, but you can find at least some different flight combination.
OTAs are a combination of different providers' travel agent services and are sold directly to you (usually via a GDS behind the scenes). OTAs are Expedia, Travelocity, Orbitz and in Germany Opodo, Last Minute, TravelScout24, HolidayCheck (apparently no bare flights) or Thomas Cook. While search engines or aggregate search various information resources to find possible links, they forward you to other sites (either airline or travel agency) to make the reservation yourself.
Among the gensets are Kayak, Momondo, Skyscanner, Hipmunk, Adioso and Google Flights. ITA' Matrix Airfare Search allows you to view fare detail and fine-tune your search using enhanced route-code. In contrast to all other search engines, there is no booking option.
Different search engines have slightly different functions (filtering, specifying complicated itineraries, choosing airline companies, finding different travel locations, making comparisons of fares if you are on date flexibly, etc.) Some are more geared towards nudist travel, other pushed hotel, auto rentals or parcels, but almost all can find several airline pairs and many can hit their EUR 3000 rate on FRA-YLW.
Under the search engines mentioned above at least ITA's Matrix, Kayak, Momondo, Hipmunk, Adioso and Google Flight can also be filtered by arrivals times. A thing that very few pages do is to mix and match different types of ticketing (i.e. listing a flight that for some reasons cannot be combined as one ticket).
For this reason, most search engines do not show a "connection" with a low-cost carrier, as they often do not process links or use third party ticket sales. At least that seems to be what at least romes2rio and kayak do in some cases (but because of the disadvantages mentioned above they will only show it if there is nothing comparable regarding prices and duration). àzair and Kiwi. com, who are specialized in cheap air travel, will also do that for you.
It makes no use for travel agencies or gensets to expand the resource to include air travel that cannot be bought, to confront travellers with many issues and not even to be that much less costly. Since your non-specified LHR link was apparently much more costly and inconvenient than most sites (including the Condor/Westjet solutions referred to by jpatocal or djhurio), there is no need for it to appear prominent in everyone's results.
However, if you break down your results, rome2rio, Google Flights or Momondo have all FRA-LHR-SEA-YLW or FRA-LHR-YYC-YLW links at EUR 1800 (at the moment of writing) that have very similar sounds. Well, if you are looking for an exhausting search machine that could find any kind of link, then, as far as I know, it doesn't work.
When there is a particular need for a different link than the ones found so far, you need to state this. Otherwise it is hard to look for them sensibly. However, the issue is not only that your search does affect several carriers, as all search engines are able to find such links.