If I have a workspace open with or without the library open (in a zone not popover, if open), and I click File->New Workspace the new workspace window comes up and the main window gets a library pane added to it. If I again open a New Workspace another library pane is added. The new workspace that comes up does not have a library. Perhaps its library is being incorrectly placed. The reason I say this is that if use the new second workspace and do File -> New Workspace from there instead of from the original one then the library is added to the newly create ws not to the one I requested it from.
This is 10.3.4.1 on win 7 x64 and I have the add library to new workspaces pref set.