Aim, I have not been in this specific situation but if I were? This is how I would approach it.
Some things I would say to your stepchild are....
1. Your mother is your mother. I am not here to be your mother or ask you to choose who you like or love more. However, because I am an adult and our father and I have created this home for us, I will have house rules for all of us to follow. Especially, until you are 18 or desire to leave this home. We all are responsible for creating a safe and loving home. So that ee grow to undetstand this home is your refuge not your battlrground. I hope this home becomes a safe place for you to share your thoughts and feelings with either your dad or myself.
2. I want to be your guiding friend/mentor while we share this home. I am not perfect but I promise you I will always be willing to talk things over or just listen. If I cannot handle you or the situation, I will tell you and I will take time out until Im ready to come back to you.
3. You dont have to love me but I hope I earn your respect.
4. You can always ask me anything. I can't promise you I will have the correct answer for you but I will do my best to respond.
Then, allow time for the everyday trust to build between you. Your step child may not love you at the moment but he may well grow to like you if you dont humiliate him. That is, show him how you value him.
I hope that helps in some little way.