For this type of task, use Windows Explorer (or any utility specifically designed for copying/moving/archiving). It will generally be a more robust solution, esp. when handling error situations.
1. Remove from Auto-Import paths that point to the old location.
2. Disable Fix Broken Links in Auto-Import
3. Quit MC.
4. In Explorer, copy the folder from the old to the new drive.
5. Launch MC.
6. Use the Find/Replace tool or Rename, Move & Copy tool (in Update database mode) to change the drive letter / destination folder (as needed) from the Filename fields for the moved media. It is this field that is the reference to the location of the media files.
7. Return the settings to Auto-Configure (add the new media path, Fix Broken Links).
8. When you are sure the copy worked correctly, then you can delete the originals.
The reason you don't want to try to make these moves in MC's general views is that you are only asking MC to move the files it knows about (i.e. those in the library). When there are other files in the media folders (e.g. log files, extra cover art, text files, ...), MC will not attempt to move those, and so you're left with two non-identical folder trees, where the original has stragglers which you must manually move. When these stragglers exist, MC cannot delete the folders (which you were hoping would be empty now, because the files were moved).
The situation is better in Drives & Devies > Explorer, as MC is dealing with the actual files in the folders. But its error handling/recovery may not be as robust as that of Explorer directly, or other archiving tool.