You could always use messenger, on two accounts that are secret. The patient will need a computer in the room. Messenger Plus! should be installed on this account, and it should be set to allow the other account to have webcam start automatically.
However, you could always simply use
ultravnc and simply start the camera viewer program on the pc using that, and view it from there.
I agree, there should be a program to do this more easily, but I personally don't know of one.
However, there's always scripts and such which will broadcast your webcam on the internet. All you'd need to do is run an apache server on one of the computers, and connect to the broadcast feed from the other computers in the house. To make sure nobody else sees it, you can block the http server ports on your router, or you can use .htaccess to require a password to view the webcam.
Just my ideas.