The 12V from the big PSU should go only to the top of the 12V relay.
If you want to run the Arduino on 5V (bypassing its internal regulator), feed 5V from the big PSU to the 5V pin on the Arduino (look at the Arduino documentation). Do not connect anything to the DC input pin of the Arduino.
If you want to run the Arduino on 12V (utilizing its internal regulator), feed 12V from the big PSU to the DC input pin on the Arduino (look at the Arduino documentation). Do not connect anything to the 5V pin of the Arduino.
The Common (0v) from the big PSU should connect to the emitter of Q1 and to the GND pin on the Arduino.
A single wire from an Arduino port pin to R1.