Wouldn't transit in YVR because it adds another stop.
If ticket costs aren't an important consideration, I would avoid transit through the U.S. on the way back (just adds to the hassle) if you are considering such a routing.
Not sure what the schedule is but KL via AMS isn't a bad option as far as an easy transit goes, and AMS has rest and play areas for families. CX via HKG is also another one-stop option with a relatively-easy connection. Not sure how the schedules for the Gulf airlines are.
Not sure how good the other airports in Europe are (I think BA requires a terminal change at LHR - not something fun even for the child-free).