I know this structure
I'd rather you... - when you want somebody to do something.
But the problem I have is the following. Can I say this: I'd rather you went to Canada than America. Is this correct?
Yes, "I'd rather you went to Canada than America" is correct.
But be careful. "I'd rather you ..." is not used when you just want to say that you want somebody to do something: If I want my brother to phone Fred, I don't say, "I'd rather you phoned Fred." "Rather" is used when you would prefer one thing to another, as in your Canada vs America example.