I created a new user and set up the private directory and it worked as the way it should, so I went into my home directory and deleted .Private and .ecryptfs and set up a private directory and it now works correctly.
I now have run into another problem. Before leaving my home directory I umounted the private directory, then logged in as my other user, the private directory was not mounted, so I mounted it using one of the scripts I created to mount and umount the private directory. I then switched users to my main user and the private directory was mounted and accessible. So when a user mounts the private directory in their home directory, all private directories get mounted system wide.
I created a new user and set up the private directory and it worked as the way it should, so I went into my home directory and deleted .Private and .ecryptfs and set up a private directory and it now works correctly.
I now have run into another problem. Before leaving my home directory I umounted the private directory, then logged in as my other user, the private directory was not mounted, so I mounted it using one of the scripts I created to mount and umount the private directory. I then switched users to my main user and the private directory was mounted and accessible. So when a user mounts the private directory in their home directory, all private directories get mounted system wide.
Mount script: private
#!/bin/sh
mount.ecryptfs_
Umount script: ecryptfs_ private
#!/bin/sh
umount.