How the heck do you have two identically named folders in the same place? Or are they in different locations?
With FTP, you can start by going inside that directory, then deleting folders one by one and see if it's one of them that has the stubborn file or folder. Then crawl down the stubborn folder deleting subfolders until you track down exactly where the file/folder(s) are that are giving you trouble.
It may just be a permissions issue with something that's Read Only for you, or even owned by another user or DreamHost robot.
If you can log in via shell, you can carefully type in:
/bin/rm -rf moodle.millermc.net_moddledata
But make sure you spell it moodledata, if that's what it's really called, and make sure it's really the folder you intend to delete.