Hi handmade film:
You can try granting (to the users in group X) permission to broadcast messages to other groups of users. This works, but might not be restricted enough to define to which groups can they broadcast. With the current Tiki implementation of broadcast messages and the permissions system, they might spam all users in your site with email messages, etc. See http://doc.tiki.org/Inter-User+Messages#Broadcasting
Another approach would be to use the capabilities to send emails to users listed in a PluginTrackerList (see http://doc.tiki.org/PluginTrackerList#More_information_on_parameters and tab "Checkbox"), and somehow, allow a user to display only certain groups of users thourgh the system (using PluginTrackerFilter ). This would work with current Tiki features and code, but you need to to master Trackers first, which is something you would be willing to learn anyway sooner or later ;-)
To learn how to master Trackers, a good starting point would be to play with several profiles from the Profiles Wizard first, in a testing environment of yourself (a localhost setup in you personal computer, etc).
And welcome to the Tiki Community!