I'm not totally clear on whether you have 3-DNS (v4) or GTM (v9), but in either case the same principle should work, if you have the 2 GTM's in a sync group, and they are monitoring the 2 LTM's, they should be able to use the Global Availability metric in a standard config to have DC1 as the primary LTM and DC2 as the backup. You wouldn't have to "flick a switch", GTM just begins handing out DC2 LTM addresses if the LTM in DC1 fails.
It doesn't matter where the devices are as long as they are able to monitor the LTM's on their public-facing interfaces (using iQuery on port 4353 as well as ssh-22 and https-443).
Denny