Each Tech Group can only have one Group Manager, so i can see how if you have 2 people in what you consider to be that role (Software Coaches) that the system may not work for you as designed.
One way of working around it might be through creation of one or more Action Rules that can say, for example:
Check all tickets when they are made for certain criteria:
If the Ticket is Request Type Software->Google Mail AND Location is School2
THEN do an Action to modify the ticket and set the Assigned Technician to Tech B
of course, that is an action that would kick off after initial ticket creation so for a (very) short time period it may be assigned to the 'wrong' Tech until the Action Rule reassigns it.