You are using the relay in non-isolated mode, making its opto-isolators redundant. This may be making the interference you see more likely.
Normally the supply to the relay module would be separate from the logic board.
If you only connect the 5V and digital pins between Arduino and relay module, and remove the Vcc jumper, then the Arduino is only connected to the sending side of the opto-couplers. Well, that's true for most of the relay modules - perhaps you should identify the one you have.