Moving a custom domain from one site to another site in Brandcast is a very easy process, but will cause a little downtime as you switch things around so make sure you're making the change during off-peak hours. When you're ready to transfer the domain between sites, follow these steps:
Open the site that has the domain, go to Website Settings, delete the custom domain, save changes, and publish your site.
Open the new site, go to Website Settings, add the custom domain, save changes, and publish your site.
Now it's very important to make sure that the Save Changes button in Website Settings changes to Saved before your publish, otherwise the change won't happen. If the button takes to long to change from Save Changes to Saved, refresh the app and try again.