How to map AD Domain Admins group to Ubuntu admins
Likewise (or PowerBroker, whatever they're calling it now) lowercases translated group names, in addition for the space character replacement that you've accounted for. Try:
%HOME\\domain^admins ALL=(ALL) ALL
Also, is it set to assume default domain? If so, then you don't want the domain part (I think this behavior started in a fairly recent version, so that might be part of it). So, also try:
%domain^admins ALL=(ALL) ALL
It's safe to just stick both of these in the sudoers file - one or the other should do the trick.