http://itween.pixelplacement.com/

Look at the "callback functions" demo.

Not sure if that's what you want, but to check if Point C was reached you can use a Trigger. (Collider that is setup as a trigger) To move something from A to B over a fixed amount of time you can write a Coroutine which is starte when Point C is reached. The coroutine would look something like this:

IEnumerator MoveTo(Vector3 start, Vector3 target, float time) {
  float startTime = Time.time;
  while (transform.position != target) {
    transform.position = Vector3.Lerp(start, target, (Time.time - startTime) / time);
    yield return 0;
  }
}

To start the coroutine the trigger object will need a script like this:

void OnTriggerEnter(Collider c) {
  c.GetComponent<MyScript>().StartCoroutine(MoveTo(start, target, time));
}