Output Signal From Digital Pin to Switch Relay, Suggestions?

Re. reply #2 schematic.

return current path for the emitter

The return path is to the 5 volt supply ground not the 12 volt supply ground.

Arduino ground and the transistor's emitter are CONNECTED

The transistor is referenced/powered from the 5 volt supply not the 12 volt supply.

I said: there is no reason to connect the 12V GND to the Arduino GND.