I thought I might offer my experience just in case noone has a picture of the daybed.
We stayed at the Yacht Club last year, and the daybeds don't actually "open up". You just remove the cushions from the back of the sofa and the bottom cushion is flat and all one piece, so that is what you put the sheets/blankets on. My 3yo daughter slept very well on it.
I could be wrong, but in the pictures that I have seen of the Boardwalk rooms, the sofa/daybed is possibly the same. Hope this helps!