osTicket should just have an SMTP setting somewhere in the script admin, along with a mailto (Google) on where to send it.
From what you mention, osTicket only allows one admin? (Not used it myself to confirm.)
And then it can only email that one admin?
Okay, no problem. To send to more than one person, create a mail list (distribution list) and send to that. That will forward emails to multi users as needed. I do this myself for several needs.
In cPanel, you can also simply add a forward more than once. For example
Code:
john@domain1.com = admin@domain
sam@domain2.com = admin@domain
Just note that the single account details can be edited by anybody with access. For example, to reset password via email. But that may not be a concern for you, if there's truly several folks sharing the admin duties.