Change domain from one site to another

I have the original domain on which multisite is set up: http://www.cityofpalmview.com
This domain has its site content that was created a while back.
I created a new site to work on a new site for them under http://www.new.cityofpalmview.com
How can I now point the original domain to the new site? I have installed your domain mapping plugin but I am not sure if this is something that can be done with the plugin or I have to do on the cpanel. I appreciate your help.
Thanks.