CtdeBlesse
The error message you are getting is a gmail error.
The gmail mail servers are unhappy with your domain address as it is not resolvable.
The error is not really sme servers fault, it is gmail being strict.
Mail sent via your isp's mail server should be OK, so I wonder if you have really set sme server up correctly ?
Perhaps your isp is not considered trustworthy enough by other mail servers.
It is bad policy to use domain names like mydomain.local etc, it is far better and avoids various issues by using mydomain.com etc even if it is not real, but better still to get a free domain name as a minimum.
You can get a free domain from dyndns.com and that may be better to configure your sme server with eg yourname.dyndns.org or whatever you choose.
Alternatively configure it with your business domain, that may work better.