So, if you want to copy /pathtodirectory/original/ to /pathtodirectory/copy/, and /pathtodirectory/copy/ already exists, you're going to end up with /pathtodirectory/copy/original/
If you want the end result to be /pathtodirectory/copy/, with all of the files and directories under /original/ now under /copy/, /pathtodirectory/copy/ shouldn't exist before issuing the cp commnand.
Also, don't use the * as a wild card to copy the files, or else you won't get the hidden files.
cp -rRp /pathtodirectory/original/ /pathtodirectory/copy/
(where /pathtodirectory/copy/ does not previously exist)
Hopefully, someone far smarter and more knowledgeable than me will come along and show some method to recursively copy into an existing directory. I'm stumped.