Apache and mod_rewrite
Using Apache's mod rewrite module I was able to do this but only because I finally found the following helpful forum thread:
http://www.webmasterworld.com/apache/3361785.htm
Here's the example of how to write the .htaccess code for it:
Options +FollowSymlinks
RewriteEngine on
RewriteCond $1 !^old_index.php
RewriteCond %{HTTP_REFERER}^https?://([^.]+\.)*thisotherdomain\.net
RewriteRule ^(.*) http://mydomain.com/old_index.php [R=302,L]
The first rewrite condition is needed because Firefox originally complained about an infinite loop. Interesting, it was much easier to find examples on the Web for this little Apache magic when setting up a redirect based on NOT coming from a specific domain. The example above is nice because it will redirect even if the referring link is from a domain or subdomain on http://www.thisotherdomain.net. Also, it is important to remove the "$" pattern end anchor that I normally place at the end of RewriteCond statements in my .htaccess files.