How to read potentiometer value in existing circuit
I'm guessing your circuit is using a 555 timer. These work by charging up C via R1 + R2 + R3 until the trigger threshold is reached (about 2/3 supply) and then the DIScharge pin is pulled low. This causes C to discharge through DIS and R1 until THReshold reaches about 1/3 supply at which point DIScharge is switched off and the cycle can repeat.

Your scheme won't work well because the voltage at the junction of R2 - R3 is oscillating. Instead, you can monitor the 555 output and do some timing measurements.

The big question: why are you using a 555 when you have a micro-controller? Feed the potentiometer into an analog input and control the output duty cycle with that instead. You may need a transistor to switch the relay but that's about it.