Joomla module/component to mass email members of a group

I need a button on my page that shows only to members of the "Group Admin" group that says simple "email all members" (see attached for a mockup). I want an email window to open up with subject and contents only, and when sent, I want it to be sent to all members of the Group Admin's group. So, it will have to send to all members of the main group that this person is a member of (including new members and excluding expired members, so it will need to check against the current list whenever an email is sent). The Group Admin person will also be a member of the particular group he is admin of and that's who the emails need to be sent to. For example, Bill is Group Admin of the Hamilton Group. When he's logged in to the site, he needs to be able to click the "email all members" button to open an email that he can send out to all members of the Hamilton Group - and no other group. This is a Joomla 2.5x site. I need an installer that I can use on other similar sites, and this cannot customize core joomla files. The button must only appear to members of the "Group Admin" group and must automatically be added to all Group Admin group member's page as per the attached, and automatically email all of the members of the other group without user interference. I hope that makes sense!