There exists a Wordpress website which has an SSL certificate for those non-www pages. So, we have attempted setting the Wordpress address Hyperlink to https://mydomain.com within the General Configurations screen. The redirect works by trying entering www.mydomain.com, only once you accept the certificate around the untrusted connection. So it must run the redirect before it inspections. Additionally, it does not appear to redirect if no 's' is put into the http, but I have found plug ins that say they'll fix that, but nothing appears to repair my other problem.

Detailed explanation: http://noctis.de/archives/11-Using-WordPress-with-SSL.html :)

Maybe you have to add yet another VirtualHost in order to buy an wildcard certificate.

<VirtualHost my.ip:80>
    ServerName example.com
    ServerAlias www.example.com
    RedirectPermanent https://example.com
</VirtualHost>

Or consider adding an .htaccess file:

RewriteEngine On 
RewriteCond %{SERVER_PORT} 80 
RewriteRule ^(.*)$ https://example.com/$1 [R,L]

Source: http://www.besthostratings.com/articles/force-ssl-htaccess.html