It's very easy to move things from one tank to another, provided that you're trying to move tank ornaments or the seahorse (you can't move the things that install into all three tanks). To move things from tank to tank, just grab the object (or seahorse) and drag it to the tab for the 'target' tank until you see the tab light up. Then release it, and it will move to the new tank. If you switch tanks to the new tank after you let go, you can see the object drop into the tank.

Sometimes it doesn't work the first try, but once you get the hang of it, it's not too difficult to move things between your tanks.