Let me start with I have never tried moving a switchover pair after it was built so I'm just guessing here. From the way I understand it switchover looks for host names so as long as the server name does not change it should not matter if the IP address changes. Alternately check the Server A and Server B address server parameters to make sure the IP addresses are set correctly.
Now since you are moving the server a DR site I assume this means the buildings are going to be geographically separated with some sort of (slow) link between sites. We have ran into all sorts of quirky issues when you introduce the potential of delay between switchover pairs. To try to alleviate the issues you are going to want to look into the optional switchover server parameters, pay special attention to the Switchover NetTest A, B, and Timeout server parameters. The net test settings can save you if the network connection goes down and you have a switchover when one is not needed. The other optional switchover server parameters may be required if you are getting switchovers for no reason.