I think ISPConfig does not understand both IPs for my domain!!!
Yes you're right, you have to add the address 10.1.1.25 to ISPConfig and then change the private site to that address.
You can do that by following the steps:
1. Logon to ISPConfig and go to the Management tab.
2. Go to Server and then Settings
3. Add the new IP (10.1.1.25) in the IP list and click Save.
4. Go back to the ISP Manager tab and locate your website.
5. In your website, click the IP Address drop down menu and select the new IP and click Save.
When ISPConfig updates Apache then your new website will be accessible inside the network. One note of caution though. you don't want the private site's DNS to display the private address to the public. The less hackers know about your network the better.