I have seen this problem before, nothing to do with our module.
Our module sends email via the DNN configured SMTP mail server. You must have permission on that server to send to the domain or email accounts.
I have seen it before where you cannot send mail to your self from your self. i.e. email@example.com to firstname.lastname@example.org – basic spam filtering sometimes stops this.
I have also seen some mail servers not like a relay from a second mail server to a local domain. Exchange chokes on this one.
Basically all I can suggest is that you resolve the mail server conflict you have on your SMTP server. Test using the same email address for the host login account and use the DNN send test feature in the host settings. Once you resolve your mail server to allow this, you should be good as gold.