The stake president will refer you back to your Bishop, because he is the one who is specifically responsible for you. It is warming to know that you have a great Stake President. He has given you the right counsel to talk to your Bishop, he holds the keys and is the Judge in Israel for your ward. As Bishops, strict confidentiality is something that is taken very seriously. Since your Bishop is your dad, he will most likely encourage you to talk to your mom about it. Anyone else will not be told, it is not anyone else's concern.
Do not hold yourself emotionally and spiritually hostage. The Lord's sacrifice was exactly for this, for you. He knew we would fall short. Out of love, no other reason, because he loved us first. The pain and anguish you feel now is nothing to what he endured and he has specifically mentioned that he took our place, so if we would strive to do our best and humble ourselves and repent we will not have to endure this pain.
Take the step, it is the price we pay for transgression, but how sweet and liberating is His grace and forgiveness.:) This will be the first step, as you peel off the layers of unknown pride, you get to the core and essence of your spirit and then the forsaking and the repenting can truly begin.