Try looking at create database for attach.
You cant restore a database with the same name as an existing database - but you can restore it with a different name, apply the transaction logs, stop connections to the original, backup its tlog and apply that to the new one, then rename both. Which if you get right would only be a couple of seconds.
One caveat to detaching databases to move them - Logshipped databases dont seem to like this - if you attach a standby database it seems to get fully recovered. Less than ideal. Anyone know a way around that?