Best thing to do is to stick with all one carrier, if you can't do that then stick with two carriers from the same alliance. Two airlines from two different alliances is a recipe for disaster. And as west jet is a low cost carrier they have no alliances.
So as they are a low cost carrier they did right by getting you to your destination. They don't care whether your happy about it or not.
I'm assuming you went with that convoluted routing to save money? (I say that because BA could have done it with one stop through Heathrow , and probably more one stop options as well) you can't have it both ways. Take the cheaper riskier option and hope things don't go wrong or take the more expensive safer, convenient option