I bought a round-trip ticket from Vancouver to Toronto. I am now in Toronto, but due to family emergency I need to go back to Vancouver and then come back to Toronto. In this case, can I purchase a new round-trip ticket in Toronto, or do I NEED to reschedule my ticket (going to Vancouver) and once I am in Vancouver buy another round-trip ticket? I am purchasing WestJet for both round-trip tickets. Isn't it more convenient to buy another round-trip ticket back to Vancouver?
If I understand you correctly, you're flying four legs in total:
A: Vancouver to Toronto B: Toronto to Vancouver C: Vancouver to Toronto D: Toronto to Vancouver
You already have a round-trip ticket for A+D, and you have just discovered that you need B+C.
Buying A+D and B+C instead of A+B and C+D fits the pattern of back-to-back ticketing, and airlines have been known to frown on that.
However this is mostly in cases where buying A+D and B+C is cheaper -- such as if there's a Saturday night between B and C and the airline offers cheap round-trip fares when there's such a night between the outbound and inbound leg (because that way they can attract pleasure travelers who wouldn't otherwise go, without needing to offer the same low price to business travelers on short trips within the working week).
If the airline you're flying with does not offer such deals in the first place (they have become less common than they were 10 or 15 years ago) -- or if you're not getting a good deal for B+C anyway, such as if you need to buy it on short notice -- it is unlikely that the airline would have any problem with it.
In any case, even if the airline does take offense, it is extremely unlikely they would refuse to transport you. At worst they may get stingy with frequent-flier points, or demote any preferred status you may have in their bonus program -- but if you're not a frequent traveler anyway you could just decide not to care about that.
You can buy a new Toronto to Vancouver return ticket and use it. There are no rules that force you to reschedule your original flight.