Make sure that mod_proxy is on, and that Apache listens on port 10001
Allow from mynetwork
Deny from all
ProxyPass / http://www.me.com/
ProxyPassReverse / http://www.me.com/
If you want, I think you can remove <VirtualHost *:10001>.
for apache 1.3
for apache 2.0
NOTE: There may be severe security implications to this setup, as, on the real server, all proxied requests will seem to come from the proxy, not the original visitor. Make sure you have good access control set up on your proxy.