Hello...
If I understand your question correctly, you cannot do what you are trying to do.
By saying "I have a domain name inside my network of xxx.net", I presume you mean you have a local DNS server with an entry for xxx.net pointing to some server on your LAN. And, by saying "I have a similiar name for a website of www.xxx.net outside my network on the internet", I presume you mean there is a domain xxx.net registered on DNS servers in the Internet. And, you have a web server on another server on the Internet.
By having a DNS entry on your local network of xxx.net pointing to a local server, clients on your LAN cannot see the xxx.net that exists on the Internet. On the Internet, xxx.net resolves the the IP on the Internet. On your LAN, xxx.net resolves to the IP on your LAN.
I suggest you rename your local network to yyy.net so clients on your LAN can use domain names to access both servers.
Did I understand your situation correctly? Did I help you with your problem?
-----Steve Jackson
CEO/CSA
Software Corporation (Softcorp)
http://www.softcorp.us/probono
Advanced pro bono tools and utilities free for personal use