I understand that your external HD is NOT showing on the folders panel, so you cannot move your photos. The trick here is to click on the "+" sign of the folders panel header and select Create Folder. A Explorer/Finder window will pop up, that will let you navigate to your external drive, where you will create a folder. Click create and from now on the external HD will be in LR panel and you can rearrange your photos. Be aware that LR moves (not copy) files even across drives.
HTH
