Apology seemed real enough to me. Although I still wouldn't have accepted it.
This is typical Yuki, he's too soft and compassionate to stay mad at someone (yeah, I'm agitated that he forgave him too, but I saw it coming). To look at it from another perspective, by forgiving his father, he could have taken an important step in accepting her mother's death, and moving on (sitting in your bedroom staring at pictures of your mother all day isn't healthy). BUT considering the circumstances he's in...well, guess I'll get to see Yuki's awakening in the next chapter and see what he does next.