As you've discovered, the home screens can be fully customized to your liking. You can add, subtract and move around shortcuts and widgets, and widgets can also be resized. I highly recommend reading the Nexus 7 user's manual, which is included in your Play Books library. It will describe all the basics. There are also many tutorials on the Web.
In the meantime, here is what to do to place the missing widget back to the home screen. I think, but am not certain, that the middle home originally contained the My Library widget. This is how to get it back.
1.Tap the All Apps button (circle with six dots inside), which is in the center of the bottom dock . The All Apps screen will appear.
2. Go to the widgets section.
3. Swipe until you find the widget called Play - My Library.
4. Tap and hold the widget. Within a couple seconds the home screen will appear behind the widget.
5. Drag the widget to the location and home screen you prefer. I think the Library widget takes up the entire screen, so once it's on the middle home screen, simply let go of it.