Symlink not updating as expected when using an absolute with relative path

I am trying to use symbolic links. I did some reading and found the following commands:

Creation -> ln -s {/path/to/file-name} {link-name}
Update -> ln -sfn {/path/to/file-name} {link-name}
Deletion -> rm {link-name}

Creations and deletions work fine. But updates do not work. After performing this command, the symlink becomes invalid.

I have read here and there that it is not possible to update/override a symlink. So there is contradictory information on the net. Who is right? If a symlink can be updated/overridden, how can I achieve this?

Update

Here is my directory structure:

~/scripts/test/
~/scripts/test/remote_loc/
~/scripts/test/remote_loc/site1/
~/scripts/test/remote_loc/site1/stuff1.txt
~/scripts/test/remote_loc/site2/
~/scripts/test/remote_loc/site2/stuff2.txt
~/scripts/test/remote_loc/site2/
~/scripts/test/remote_loc/site3/stuff3.txt

From ~/scripts/test/, when I perform:

ln -s /remote_loc/site1 test_link

a test_link is created, and I can ls -l it, but it seems broken (contrary to what I said above in my question).

How can I perform a multiple directory level link?