shamrami,
Sounds like you have guessed the reason for your nuisance tripping already. 1/2 a mile (800 m) is a long distance and it is very well possible that the capacitance of the wires play a role here. This wire represents around 50 - 150 nF of capacitance (depends on cable type and area) and that can easily pass a substantial current that trips the relay. Sometimes you even get a resonance between cable capacitance and relay coil, but that usually makes the relay stay activated when the distant switch is opened. It seldom pulls the relay in.
If your relay is a small one with low coil current, it is a good idea to try a small contactor instead. They are much less susceptible to this problem.
The easy way to get rid of the nuisance trips is to put some extra load parallel to the relay coil. An incandescent lamp usually works well. If you put a 15 - 40 W lamp across the coil, you sholdn't have any problems at all.
But, you have to be careful. If it is important that the circuit trips when it shall (usually very important) you should A) Check that tripping takes place also when the extra load is added and B) Make sure that a short in the lamp does not blow the fuses in the trip circuit. A small extra fuse (0.5 or 1 A) in series with the lamp is wise to have. If you select too high a melting current, it is possible that the fuse doesn't blow. The short will then load your trip circuit instead of being cleared by the fuse.
If you want to do something a little more elaborate, you can change to DC and use a DC coil and a DC rated contact in the signal path. It is more complicated and not always possible to find a DC coil with the same dimensions and function.
