You’ll need to set the new location in iOS Scrivener. In version 1.0, moving the folder caused a crash. This may be fixed in the latest version, but unlinking Dropbox first is sure to be safe.
I would do these steps, in order:
Make sure everything is fully synced.
On both iOS devices, use the Unlink Dropbox command under the Gear icon on the project screen.
Close Scrivener on the iOS devices and leave them alone for the duration.
Do whatever shuffling you want to do on the desktop. Make a backup outside of Dropbox.
Close desktop Scrivener. Allow Dropbox to synchronize with the desktop.
Launch Scrivener on one of the iOS devices. Relink Dropbox. Allow it to sync. Confirm that everything is fine.
Repeat on the other device.
Most common cause of errors? Incomplete synchronization. If you moved a lot of material, re-syncing could take some time. Be patient.