Apache :: Internal Server Redirection Vhost

I have a Public [82.x.x.x] and Private Apache Servers [192.168.20.100], and wish to redirect a series of subdomain requests i.e. for joomla.example.com or moodle.example.com on 82.x.x.x => joomla.example.com or moodle.example.com on 192.168.20.100.

joomla.example.com [82.x.x.x] returns joomla.example.com [192.168.20.100]

moodle.example.com [82.x.x.x] however returns joomla.example.com [192.168.20.100]

VHOST Configuration on [82.x.x.x]:

<VirtualHost *:80>
ServerName joomla.example.com
RewriteEngine On
RewriteRule ^(.*)$ http://192.168.20.100$1 [P]
</VirtualHost>
<VirtualHost *:80>
ServerName moodle.example.com
RewriteEngine On
RewriteRule ^(.*)$ http://192.168.20.100$1 [P]
</VirtualHost>

----------

VHOST Configuration on [192.168.20.100]

<VirtualHost *:80>
# joomla.example.com>
ServerName joomla.example.com
ServerAlias joomla.example.com
DocumentRoot /var/www/joomla/
ServerRoot /var/www/joomla/
ScriptAlias /cgi-bin/ /var/www/~cgi-bin/joomla/
ErrorLog /var/www/~log/joomla/error.log
CustomLog /var/www/~log/joomla/access.log combined
ErrorDocument 404 /404.htm

[Code] ......