Hello anonymous user ,
Thank you for posting here.
Basedon the description above, we want to a dedicated team group have local Administrator right on all the member server of all the domains (including root domain and child domains), if I understand it right, I think the way you are configuring is very good. Because it can meet your need and we can set it in batches.
We can use one of the group policy settings:
Computer Configuration\Policies\Windows settings\Security Settings\Restricted Group
Or
Computer Configuration\Preferences\Control Panel Settings\Local Users and Groups
Hope the information above is helpful.
Best Regards,
Daisy Zhou