The problem is that you aren't using Libraries correctly. Libraries are only picture icons that represent the actual files that reside in your User folders.
Libraries aren't made for the stardard drag and drop file movement and there are good reasons for this. You would be far better served to use the
User folders My Document, My Pictures, etc. to move those files around using the drag and drop method.
You would also be better off not mixing your Public folder with your Libraries and visa versa, it's best to keep those seperate because they both work off of a different set of sharing rules. Libraries aren't made to be used for public sharing, they are only made to be used for the LAN computers which are connected to a common Homegroup using a Homegroup password. This adds an extra layer of security to the Homegroup.
You can move files inside of Libraries but you need to do it by using the tool bar on the upper left pane, it's not enabled by default. The drag and drop method does not work correctly with Libraries, it's made this way for a reason.
In case anyone wants to know how to send or copy files to and from the Homegroup Libraries there is an easy way. You need to use the menu pane for this.
One problem is that the
Menu pane doesn't show up by default but thats easy enough to change. You can also go to
folder options then
view tab and select the "
always show menus" option but that isn't checked by default either.
I'll go over the steps needed to access the
copy to and
move to folder options just so it's very clear for anyone who reads this.
With a Library open as in
Library>Documents look to the left and click on
Organize> scroll down to >
Layout then click to make sure the
Menu pane is showing. Now that you have the Menu pane checked you will see
file,edit,view,tools,help at the top of the page on the left.
Next highlight the Library folder or file you need to move or copy, then click on the
edit button in the Menu pane and
choose copy to or move to folder option, click on
Homegroup then choose the
persons name, then choose the Homegroup folder you want to sent it too and hit the
copy button at the bottom of the page. You can easily move files around between Libraries using this method.
This tutorial from Brink also shows you how.
Context Menu - Add Copy To Folder and Move To Folder