I've been through this with my own sister. There is history there -- very serious history that could have left us forever estranged.
But time has been healing for our relationship. I think we both reached a place where we know we can't change what happened, but we can share our present and future. That past doesn't have to completely cut us off from each other unless we make that choice.
I didn't have to have an apology, not directly. What I did get over time was a sense that she did want a present and future with me in her life, and I wanted the same with her. We've basically set that past asid. It happened. Keeping the past as a wall between us wasn't healthy for either of us. We essentially chose to let that history go and move forward. I guess it was a process of forgiveness for both of us.