lolcol11:
I think the problem is using the home power supply but anyway,
But that's the 12V side isn't, and the relay coil is powered by the Arduino 5V, triggered by the digital signal.
What happens if you disconnect everything except the relay module, and use a simple code like blink to simply toggle the relay in loop()?
And you should also show a proper circuit diagram, even a quick scribble in biro and a pic with your phone.