If a global service group is failovering to target site it takes down the PROD IP and brings up the DR IP. As soon as DR IP up, network load balancer(which know both IPs) should able to send the traffic to new IP. 

Regards,
Ravikumar

As the VIP can not be failed over to DR site in normal case (they are normally in different subnet),  So you have to do a dns update to make the dns entry refer the new IP.   GCO also suggests to setup dns inside the cluster, but it's not mandatory.

You can take any of the approaches based on what is available

#1 - Microsoft Servers & AD DNS

If you are using Microsoft AD DNS as the corporate DNS, then you can use LANMAN agent (for Windows Servers) to update AD during failover to secondary site, this quite simple.

#2 - Other Servers

Normally all vendors will provide the clients / agents for updating DNS with commandline (without using GUI), use VCS postonline & postoffline triggers to update DNS to the values you need after each failover. (You many need to configure SSH between a trusted server and DNS so that it can be controlled)

#3 - Using External Loadbalancer or Site Selector

Things will be much easier and hassle free if you have some thing like Cisco GSS in your enterprise. If you have, then confgure it to monitor and point users to respective server based on some condition such as application port number or VIP IP configured on the IP resource

Regards
Habeeb