You use Carbon Copy Cloner. It copies all the information from one hard drive to another.
If you change the information on one hard drive it does not change the information on the other. Think about this for a second: If you clone one hard drive to another, then take that other hard drive and disconnect it from your computer and turn it off, then delete a file from your Home directory, how can it delete the file from the other hard drive? If the hard drive is not even attached to the computer, the information on it can't be changed.
I'm not quite sure what problem you are having, but I think you are not understanding what is going on. If you attach the second hard drive and click the button called "Home," it takes you to the home directory ON THE BOOT DISK. The Home button always takes you to the BOOT DISK; it does not matter what hard drive icon you opened. Opening the second hard drive and clicking the button called "Home" does not take you to the Home directory on the second hard drive, it takes you to the home directory on the boot disk!
To get to the Home directory on the second hard drive, double click the second hard drive, then double-click the folder called Users, then double-click the name of the user you want.