Her Step-Mother - Her relationship with her step mother isn't something that pleases the girl. It isn't known to her other siblings and father but she doesn't like being around the other women. She see's her as ruthless, vain, power hungry and mean. She won't accept the fact that Hana didn't cause the love between her father and Aian. But she is seen as the source of unhappiness. Growing up, she whenever she was around her step-mother she was always verbally abused. She was physically hit by step-mother but she did not tell anyone and she would not show it. In her eyes, keep silent was more important. She was the cause of the pain of her family so she could take it.
Her father - Because of the odd match, between her 'parents', she always wondered why they ended up together. Both seemed polar opposites but she knew even if he wasn't in love with his wife, she knew her father loved his wife. Still the bond they had was stronger then anything Yubin even had with anyone. He was her star and he protected with his life. Her father always tried to make sure she was happy and reminded her no matter what she was The Princess of The Fire Nation. Even though she doesn't trust it. He knows she will. In her eyes, her father is a kind ruler, most people can't trust the fire nation, yet but they trust her father, he is kind and gentle and can make friends with anyone. His allies are everywhere, when he needs to be he is a strict and wise leader. He understands Fire is a power that breaths life and not pain. Also her father is silly, resembling both Iroh, The Old Fire Lord and The Old General, he is clam and likes to sing and be marry, he is the Fire Lord Iroh her great uncle would have been had he ascended the throne. He is a figure what will lead the Fire Nation with an iron fist but lovely heart. He is strong, smart, loving and caring.
OOC: To be fair to others in the family, these head canon's are from Hana's eyes. So if you write, we can all see him in a different light. Although I'd like them to agree on some things. Using Iroh and Azula to show how I envision them to be.