This depends a rest deal on how your server and router are arranged, so adding more information to your question will improve the chance of getting an answer that is correct for your circumstances.
If the web server has multiple network interfaces (even if they are virtual interfaces like eth0:1, eth0:2, ...), one for each gateway, and you are using curl to make the requests then you can use curl's CURLOPT_INTERFACE option (see http://php.net/manual/en/function.curl-setopt.php) to select the out going interface.
It is unlikely that your server is configured this way though - you probably have the one interface and a single address and the egres router(s) on the wider network handle deciding which packets go out over which connection. If you have control of the machine(s) that are responsible for that routing decision then you will be able to setup specific routes for specific addresses using the
route command as suggested by Rich. We would need more detail of your current network and routing configuration to be able to give more specific help than this.