By pressing the "Outgoing" button, the endpoints are dialing out whatever is in the "Outgoing Extension" field in the endpoints "Associated Extensions". This is usually a trunk group or ARS. In defaulted systems, "8" does the same thing. Sounds like your system may be using "9" instead of "8".
Since you are trying to reach other internal sites instead of outside numbers, I would leave all the existing ARS/programming as is. I would setup a new trunk group for the second PRI and give it a single extension number like "7", or put buttons on the endpoints to access the new trunk group. The system is looking for a minimum of 7 digits, so dial a # at the end of your four digit number to let the system know you are done dialing. You would press the trunk group button or "7", followed by your four digits, followed by pound (#).
You can get more creative by programming phantoms and ARS, but I would go the simple route first to make sure it's even going to work...