This is a known issue - with chargers. (Not the Fairphones fault, that is.) If you can use a charger with ground, you should not see the erratic screen behaviour.
Does either one of you have trouble with the screen without the phone being plugged in for charging? If so, you could try to boot to factory test mode (turn off, press vol down + power), test the touch screen there and see if the test produces erratic results as well.