When people genuinely feel that the other person would go the distance for them - whatever it takes - the conflict completely goes away, and all of a sudden, compromises can happen so easily. I've seen people completely reverse "firm" opinions that they hadn't budged on an iota, in a few seconds. See more here...
A study conducted by law professor Jennifer Robbennolt showed that a sincere pre-emptive repentance to an injured person in a a law suit, is more likely to bring a quicker settlement of the dispute than a partial apology or no apology at all. In the study, 73% of the plaintives agreed to avoid a court case when they received a sincere apology for what they went through from the defendant.
So now imagine that the Judge is actually your father, whose love for you has no end. That's how it is when we sincerely apologize to Hashem, He forgives us competely 100% of the time.
You can achieve awesome spiritual corrections while kindling the Chanuka lights. Have in mind that Hashem forgave you already on Yom Kipper. Nowhere is G-d's love for Israel more clearly revealed than by his willingness to continually forgive our sins. Remember to forgive yourself too before kindling the lights.
The theme of Chanuka is the consecration of the Holy Temple (chanukas beis Hamikdash), and on Chanuka you are drawing the sanctity of the Holy Temple upon yourself and your family - but you can only do this if you first forgive yourself for your sins like Hashem already did!