Hello Jeff Bradshaw,
If you add the dropped node to the target NodeCollection, the node should be automatically transferred and you will not have to delete it from the old place. Are you copying/cloning the node?
Please, try to just add the node to the new location and let me know the results.
If the node's still being on both places, please post some code which will reproduce this at our end (you can also open a support ticket and send us a sample project).
the Telerik team