Well, this is getting complex but I find it
extremely implausible that interference on the (USB) power line is causing problems as such.
Using interrupts sounds like a generally
bad idea for this application, and any interference is going to be coming in on the input signal, so that is where you need to be looking.
I see no reference to the ground connection which must be coming to the Arduino along with the input signal. Clearly an optocoupler is simply
essential in this application.
The diagrams repeatedly confuse the USB connector with the "Barrel jack".
And as an incidental aside, disconnect the potentiometer from the 5 V line. This is a persistent mistake that has infested projects virtually since the beginning! Also, given that R8 on the LCD module is "101" or 100 Ohms, the 220 Ohm resistor is unnecessary unless you actually find the LCD too bright.