Accessing Internet server through intranet

I’m building a internet site that’s going to host a web application, and had this crazy idea, the server has to ip addresses on for my local network and the other one for a DMZ, the site is currently available through a defined address that is mapped to the dmz (ex. www.mysite.com) and even local users access the site via this address is there any way to make a configuration in windows either on the DNS server or on local machines so that all computers on the intranet resolve the www.mysite.com address to the local ip instead of going through the internet and back to my local server?