Based on your description, can you provide more details about how you move your documents?
Per my test, I move through opening with explorer from ribbon, or selecting documents and moving, I do not see the duplicates of these documents in the recycle bin after moving documents.
For troubleshooting this issue, I recommend to verify the things below:
1. There are any workflows associated with the library will move the documents to the recycle bin.
2. Check if there are any custom solution associated with the library will affect the library.
3. Does this issue only occur with this library?
To narrow up the issue scope, please create a new library to test and compare the results.
4. What was the original location for the files in the recycle bin? Was it the former folder or the new folder where the files were moved to?
How is everything going?
Is there anything update about this issue?
Victoria this happens when you are moving files using: "Manage Content and Structure".
below is a extract from the support article
This feature enables a site administrator to reorganize a site without forcing site administrators to delete each item individually. Entire subsites or individual items can be deleted from the site collection hierarchy.
If the recycle bin is enabled for the site, list items can be recovered after they have been deleted. However, deleting a subsite is a drastic action; the entire branch is permanently deleted even if the recycle bin is enabled.
it means this is by design that document will appear in recycle bin if it is enabled on site. But delete site will not appear.