-#mv /home /oldhome
No need to create another /home directory.
No need to mv except it will delete everything from the old home directory.
I would verify everything has been copied to the new home partition prior to deleting from the existing /home.
Be sure to log in as root so no files in the existing home directories will be accessed.
If you mount the new home before deleting the the existing home files they will become invisible. However it will prove that everything still works. You can always unmount the new home.