Ok, so both IPs are hitting your firewall and being NATted to the same internal IP of your web server. That is the scenario, roughly, right?
Now, to get www.xxx.com CHANGED in the browser window of a user to www.yyy.com, then the user will have to hit SOMETHING to get that to happen.
You can't change the URL in a user browser window using modified DNS A records or such.
You need to have the user hit a resource on your network that REDIRECTS them to www.yyy.com.
So, here is what I suggest.Change the NATting rules on your firewall, so that www.xxx.com comes to ANOTHER IP address on your web server. This 2nd IP address hosts its own single-page web site that instantly redirects the user to www.yyy.com.
So, what will happen is a user goes to www.xxx.com. That request will hit the xxx.com web page on the 2nd IP on your web server. The page then redirects the user to www.yyy.com.
For the user, they will type in www.xxx.com, then after a moment they will see the address changein their browser to www.yyy.com, and the web site at www.yyy.com will start to load.
This is usually how it is done, AFAIK. Maybe you could do this with Host Headers, but you would still need a 2nd IP address internal and 2nd web page.
hope this helps