when it does start to move in the wrong direction we instinctively hit the brakes, making matters worse.
Which is why pilots are wise to heed the recommendations in the B737 FCTM that if landing with a crosswind on a slippery runway, a directional control problem can occur. As the aircraft starts to weather vane into wind, the reverse thrust side force component adds to the crosswind component and drifts the aircraft to the downwind side of the runway. Also, high braking forces reduce the capability of the tyres to corner.
To correct back to the centreline, release the brakes and reduce reverse thrust to reverse idle. Releasing the brakes increases the tyre-cornering capability and contributes to the maintaining or regaining directional control. Setting reverse idle reduces the reverse thrust side force component without the requirement to go through a full reverser actual cycle.
Use rudder pedal steering and differential braking as required, to prevent over correcting past the runway centreline. When directional control is regained and the aircraft is correcting towards the runway centreline, apply maximum braking and symmetrical reverse thrust to stop the aircraft. Note that use of this technique increases the landing distance.