I cannot clone my site
I would recommend that you avoid multisite, and clone the code into a separate codebase -- then copy the database. This is much easier to manage for simple use cases, and would entirely avoid your problem above, as you would only have one copy of each module present in your code base, so Drupal would not be able to load any of them twice.

I am not sure exactly how your situation above came to be, but the database from the original site contains references to all of the paths of all of the enabled modules; somehow, Drupal is trying to bootstrap both the old cached paths, and also the new paths for the same module in its new location.  If you want to continue with a multisite setup, it is likely that a registry rebuild would clear this up.