Admins and root are two separate groups so admins would never really be able to see root-owned groups, at least not the way Linux is designed.
But what you’re trying to accomplish actually works the reverse way: the people who you want to see all of them should be given their own group and then assigned supplementary groups admins and root.
So, user will should be of group will. will should also be groups to admins and root (because you can totally trust that guy).
And user Eve should be of group eve and additionally of group admins. This way she has access to any of her own servers, and then also any group owned by admins (and no access to root-owned groups).
Something like this would accomplish it:
usermod -G admins will
usermod -G root will
usermod -G admins Eve