Is it possible to create an AcyMailing tab within each group and to create and send mailings seamlessly from within the group structure to the separate constituents?
That's entirely possible for you to develop of course. I recommend using the Group Message feature if they need to send a message to all group members.
As an example, if GroupA is a school, would it be possible to create a mailing (custom school newsletter template) from within that group(school) and send the mailing to that group's teachers every Monday, parents every Tuesday and Students on Friday? The newsletters need to be created and scheduled from within the group interface, by the group creator/owner. This owner will not have administrator login to the Joomla backend.
I suppose if that's how you designed the integration to work then that's what it'd do. GJ has no AcyMailing or Newsletter integration nor is one currently planned.
Can you give some implementation pointers?
Best recommendation is reviewing existing plugins, they're structured and named very cleanly and simply use Triggers, which there is a tutorial on trigger usage at the below URL.
www.allmysocials.com/directory/tutorials/item/228-event-triggers