I think you should add an external redirection web site rule to the site document for mail.mydomain.com, with as follows:
incoming url pattern: *
Redirect to this URL:
https://www.otherdomain.com/Folder/fileStarting the redirect URL with a protocol specifier makes it an external redirect which send back the new URL to the browser (as described in the Administrator Help).
If you had read the Administrator Help (Topic: Web Servers:The Domino Web Server:Hosting Web sites:Web Site rules and global Web settings), you would have seen that putting in mail.mydomain.com in the incoming pattern is not how you should specify the rule.
if entering
https://www.otherdomain.com/Folder/file does not work, while there is actually such a file on the specified path, then look for a conflicting Web rule defined for otherdomain.com
Another possibility is Domino is running on a case sensitive OS or file system.