What is the ruling on swearing to divorce my wife if she initiates reconciliation with my sister, knowing that my sister was the one who initiated the reconciliation?

There is no sin upon you concerning your oath, even if you break it. However, an expiation for the oath is required of you, due to the saying of the Prophet (peace and blessings be upon him): "Whoever swears an oath and then sees something better than it, let him do what is better and expiate for his oath." Divorce does not occur with your statement: "And if she comes to you, I will divorce her," because it is merely a promise of divorce that does not necessitate fulfillment.