In order to have a cross-domain access to my test instance of SQL Server I need a login with a database user and not with a Windows user.
Once this would work I could start doing this from my *NIX environment, but basically Windows won't let me access the DB this way and throws an authentication error 28000/SQL Server Error 18456.
I already did
ALTER LOGIN [administrator] WITH DEFAULT_DATABASE=[...]
ALTER LOGIN [administrator] WITH PASSWORD=...
Verify that the SQL Server is configured to allow SQL Server auth (as opposed to Windows-only auth).
https://support.microsoft.com/en-us/kb/2121736
If that doesn't solve, check the State that accompanies the error message. If the ODBC connection error doesn't include that information, you should also be able to track the failed login attempts via the logs on the SQL Server to which you are trying to login.
https://blogs.msdn.microsoft.com/sql_protocols/2006/02/21/understanding-login-failed-error-18456-error-messages-in-sql-server-2005/
Where are SQL Server connection attempts logged?