You might not see the second swan as it may be taking a break from a nest. Nesting may be the obvious answer to seeing the swan in the same location continuously. If there is no nest, there is a possibility that something is wrong with the swan. Not sure if you can get close enough to see if there is a nest.

On another note, we are not sure of your location and many states will try to kill the nesting swan, especially if it is a Mute Swan. Wildlife officials are killing Mute Swans to open their habitat to bring in the larger Trumpeter Swans, for Trophy Waterfowl hunting. So, we would suggest that you be extremely cautious in reporting the swan unless you can find a reliable kill-free wildlife rehabilitation facility that might be able to offer assistance. The Regal Swan