Vi elsker hunden var." and "Vi elsker var hunden."?
Does it matter if the word var comes before or after the word for dog?
The second example should be, "Vi elsker vår hund."
"Hunden vår" and "vår hund" are equally correct, however, the first is probably more commonly used. :0)
Is it correct that the 2nd way emphasises the 'vår'?
e.g. "Det er ikke hunden hennes... den er vår hund!"
I'm from norway. Instead of "den" you want to use "det". Like this "Det er vår hund." instead of this "den er vår hund." I don't know if you think it's logical, but it's the correct way.
In your example I would say so. "Det er ikke hunden hennes... den/det er hunden vår!" could work when spoken, since you would stress"vår". But in writing, I would have written it as you did. In "Vi elsker hunden vår" and "Vi elsker vår hund" I don't see any difference. The last way is a bit rare, and sounds (to me) a bit archaic. At least when spoken.