Since there seems to be a lot of confusion about what you are looking for, it could be useful to have a summary of what has been suggested (thanks and +1 to everybody who answered!). There are several types of tools you can use to find routes combining flights operated by different airlines:
- Airlines' websites typically sell flights from other airlines (not only codeshare or partners from the same alliance but also flights that can be sold through interline agreements). Obviously there are many limitations but they can find at least some multiple airline combinations.
- Online Travel Agents (OTA) will combine products from multiple providers and sell them directly to you (typically using a GDS behind the scenes). OTA include Expedia, Travelocity, Orbitz and in Germany Opodo, Lastminute, TravelScout24, HolidayCheck (apparently no naked flights) or Thomas Cook.
- Search engines or aggregators search various data sources to find potential connections but redirect you to other websites (either airlines or travel agents) to handle the booking itself. Aggregators include Kayak, Momondo, Skyscanner, Hipmunk, Adioso and Google Flights.
- Other tools can also be useful. For example, Matrix Airfare Search from ITA lets you look at the details of the fares and use advanced routing codes to refine your search. Unlike all other search engines, it does not provide any link to book the ticket. I don't know much about it but KVS Availability Tool might also be relevant.
The various search engines have slightly different functionality (filtering, specifying complex routes, selecting airlines, exploring various destinations, comparing prices when you are flexible on the date, etc.) Some are more focused on naked flights, other push hotels, car hires, or packages but nearly all can find multiple airlines combinations and many can beat your EUR 3000 price on FRA-YLW. Among the search engines listed above, at least ITA's Matrix, Kayak, Momondo, Hipmunk, Adioso, and Google Flights can also filter by time of arrival.
One thing that very few sites do is combine separate tickets (i.e. list flights that for some reason can't be booked together as one ticket). Generally speaking doing that is a bad idea since when anything unexpected happens (delay, cancellation, luggage problem), you're on your own. Because of that most search engines won't show a “connection” that involve a low-cost airline as these often don't handle connections or sell tickets through third parties at all. Still, at least rome2rio and Kayak seem to do that in some cases (but, because of the drawbacks noted above, they will only display it if nothing reasonably similar as far as price and duration is concerned is available).
For travel agents or aggregators, expanding resources on flights that can't be sold, expose travelers to a lot of problems and might not even be that much cheaper does not make sense. Given that your unspecified connection over LHR was apparently significantly more expensive and cumbersome than the ones found by most websites (including the Condor/Westjet solution mentioned by jpatokal or djhurio), there is no reason why it should figure prominently in anyone's results. Yet, if you drill down their results, rome2rio, Google Flights or Momondo all have FRA-LHR-SEA-YLW or FRA-LHR-YYC-YLW connections around EUR 1800 (at the time of writing) that sound very much like the one you described.
Now, if you are looking for an exhaustive search engine that could find any arbitrary connection then that does not exist as far as I know. Everybody who knows something about the industry seem to agree that it would be much more difficult than you suspect (see this earlier answer and this presentation for a glimpse into the issue). Note that the problem is not so much finding a route (that's a well-known problem) but also getting all the data in the first place and coming up with a price that can be booked. All the tools listed here are designed to find actual bookable tickets, not idly explore flight routes.
If there is a specific reason why you want another connection than the ones found until now, then you need to explain what that reason is. Otherwise, it's difficult to meaningfully search for it. In any case, the problem is not merely that your solution involves multiple airlines because all search engines are fully able to find such connections.