I want both www and non-www to work !

Just removed these 2 lines from you htaccess. That part removes "www" from any request.

Code:

RewriteCond %{HTTP_HOST} ^www\.(.*)$ [NC]
RewriteRule ^(.*)$ http://%1/$1

Also, I would recommend you update your mysite.conf to

Code:

<VirtualHost *:80 >
      ServerName www.mysite.com
      ServerAlias mysite.com
</VirtualHost>

So it can detect both www and none www without issues.