mod_rewrite equiv to my current RedirectMatch

[hudsterboy]

Hi,
I currently have an Apache web server with multiple VirtualHosts. Each VirtualHosts on this server redirects the browser to another web server on another server. I am using a RedirectMatch in each <Virtualhost> like this:

<VirtualHost clientsite.mysite.com>
RedirectMatch (.*) https://fhdb3-9.mysite.com$1
</Virtualhost>

So, basically everything hitting that particular virtualhost, will be forwarded to fhdb3-9.mysite.com.

This works fine, except that I would like the URL displayed to be "clientsite.mysite.com", not "fhdb3-9.mysite.com".

Would mod_rewrite help me here? Anyone know how?

Thanks!