You could create a variable, kept on the spawned instance, that stores which 'spawner' it belongs to.

On a script attached to the spawned instance (which I will refer to as 'scriptName'):

var spawnOrigin : GameObject;

In SpawnAnother(), when you create the object, you would:

localObject.GetComponent(scriptName).spawnOrigin = gameObject;

This sets the 'spawnOrigin' variable (on the spawned instance) to the GameObject that spawned it.

You would then use the spawnOrigin variable to SpawnAnother(), i.e.:

spawnOrigin.GetComponent(SpawnTarget).SpawnAnother();

Without your full code, I can't post a complete snippet, but hopefully you'll be able to piece it together. Any questions, please ask.

The easiest would be to store the position (and rotation) of the object in the Start function, and use it to spawn the object:

(I am not a native JavaScript speaker, so the syntax might be a bit off). The following must be in the same script as the function SpawnAnother in your code.

var initialPosition : Vector3;
var initialRotation : Quaternion;

function Start()
{
  initialPosition = transform.position;
  initialRotation = transform.rotation;
}

function SpawnAnother()
{
  var localObject : GameObject = Instantiate(gameObject, initialPosition, initialRotation);
  localObject.GetComponent(moveTarget).speedLeft = myCounter + 2;
  localObject.GetComponent(moveTarget).speedRight = myCounter + (-2);
}

(P.S. I am not sure why you had gameObject as parameter for instantiate - I am assuming here that you want to clone the attached object, so I replaced it with gameObject).