Lucy and her were practically twins. They were so inseparable that during Molly's first year of Hogwarts Lucy cried every single night until the holidays. It was the worst year of Lucy's life. And although Molly missed her sister she quite liked Hogwarts without her. She liked making new friends and having some distance.
Molly's more like her father even though she looks like her mother. She loves rules and school work and is very serious. Percy fears this so much. In fact when they found the note she'd left the night she ran away, Percy was angry at himself for not knowing she would do it before. After all it was the exact same thing he had done, except he had deserted his family for a job. She abandoned school, her friends, her family and her whole life to defy expectations.
She couldn't STAND the expectations put on her because of her father. It drove her to abandon her life. She ran away after her 5th year and went to stay with her aunt on her mother's side in New York. When he parents found out where she was she BEGGED them to let her stay. She didn't want to go back to London where everyone expected so much out of her. She wanted a chance to become her own person.
She regrets the cruel things she said to Lucy the day before she ran away. Molly just wanted some separation. She ended up screaming that Lucy trailed her like a dog and she was incredibly annoying and that's probably why she doesn't have any friends. And when Lucy started to fight back. Molly did something she will never forgive herself for, she slapped her.
When she returned to complete her 7th year at Hogwarts, she felt like a stranger. Everything had changed, she didn't belong anymore. Even Lucy had new and better friends on the quiditch team. But even so she does not regret coming back; she needed to make it up to her family. Especially Lucy.
The first quiditch match she saw Lucy play at, she cried. She was so incredibly proud. And then she realised that even though she regrets what happened between them it pushed Lucy to get her own life, a better life.
The night Lucy forgave her was the best night of her life. When Lucy told her that she was her sister and although what she said hurt her she was thankful to her for leaving because it inspired her to be better and that she forgave her. That weight of guilt on Molly's heart was completely lifted. She had her sister back.
When she told her father she was training to be a heeler she was terrified. She thought he'd be disappointed that neither of his daughters went into the ministry like him. But he was happy. He told her he loved her no matter what she wanted to be. That night Molly felt so completely relieved that she broke down.
She's always missed that closeness she and Lucy had before the fight. She misses being inseparable and being almost twins. She regrets not appreciating it more when she had it.
Her aunt was the one who encouraged her to go back. Her aunt saw that she ran away because she was having a breakdown and it wasn't going to get better until she went home.
