DNS and URL Mapping
Solution 1:
AFAICS you need to reverse-proxy connections for that.
ProxyRequests Off
ProxyPreserveHost On
<Proxy *>
Order allow,deny
Allow from all
</Proxy>
ProxyPass /sitename/ http://serverA.com/site/
ProxyPassReverse /sitename/ http://serverA.com/site/
See here for a more detailed explanation, and here for the mod_proxy documentation.