title: Handling email to/from a custom domain in GMail, while retaining the record in the custom domain
body: <p>I have a regular GMail account and an account at my domain (hosted by Bluehost), lets call it guest@mydomain.com. I would like to be able to handle all my mail from GMail, but have a record of received and sent mail in <code>guest@mydomain.com</code> as well. So, I configured my GMail account to send as <code>guest@mydomain.com</code> and unset the <em>alias</em> checkbox.</p>
  <p>There are two issues I'd like to resolve:</p>
  <ol>
  <li><p>Emails that I send as <code>guest@mydomain.com</code> from GMail appear only in the Sent Box of GMail. Is there a way to make them appear in the Sent Box of <code>guest@mydomain.com</code> as well?</p>
  </li>
  <li><p>Emails sent to <code>guest@mydomain.com</code> do not appear in by GMail inbox. I realize that they would appear there if I check the <em>alias</em> option. However, this seems to contradict the way I want sending to be handled (as per the first issue above).</p>
  </li>
  </ol>
  <p>So, is there a way to fully handle email to and from <code>guest@mydomain.com</code> in GMail, while retaining the record in <code>guest@mydomain.com</code>?</p>