You'll need to remove that domain from the first management group before it can be added to the second. That may be somewhat tricky if it's not actually showing up in the list of managed objects in the management group. It may require you to remove both domains from the management group, and then add back the first domain. Then you can add the second domain to the second management group.
But perhaps not... in my console, the "Managed Domains, Workgroups and Update Servers" tab of the management group displays the domain in AD format. If both domains are not listed there, navigate to the Patch Manager System Configuration node, and open "Scope Management" from the center pane. They should all be listed under "Active Directory Domains and Workgroups". Select a domain, and the details pane will display attributes of that entry, including the NetBIOS name and the assigned management group.