Moving home directory between who PCs

I use two PCs at different locations and wish to "move" my home
directory
between the locations by means of a usb memory stick.

The idea is to link my home folder to the usb memory in both PCs ("ln -
s
/media/usb_memory/my_user_name my_user_name") in the /home/ directory.
I use
the same user name and password in both PCs.

This works fine when initializing PC1. When I start PC1 I can login
with
password as my_user_name and the folder in the usb memory is
accessed.

It is however not possible to login into PC2 (with the usb memory in
place in
PC2). The login procedure is rejected.

By "swaping" the procedure (initialize PC2 ant try to log in into PC1)
the
result becomes the same. I. e. I can login into PC2 bot not into PC1.

Is the login procedure PC name (host name?)
related?

Is it possible to move the home directory in the way I wish and, if
so, how and where shall I make
"corrections"?

.

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