I suggest just measuring the LDR without it being connected to the comparator.
Do you need a relay? If not, circuit A would work.
Since you are remoting the LDR at the end of long twisted pair wire run, I have a couple of suggestions. First, add some hysteresis to the comparator by connecting a 470K resistor between the comparator output pin and the + pin.
Second, I would add an 10uF 20V-50V electrolytic capacitor between the Vdd pin (+12V) and the Vss pin (gnd).
Third, add a 1uF capacitor between the - pin and gnd.