just found out about the bleach novels. might read into them. they give some info between aizen's defeat and ichigo getting his powers back. also explains why rukia cut her hair short.
In Rukia's flashback, she was in shock when she first saw the picture of Hisana because of their similarities (at this point, she was unaware of having a sister). She thought Byakuya really loved Hisana, otherwise he wouldn't have adopted a Rukongai citizen like her, who looked similar to his wife. Rukia decided to become Hisana herself in order to repay him for his kindness until decades later, when she finally learns the truth behind her adoption.
Therefore, on the day of her Vice Captain promotion, Rukia cuts her hair, because she knows she has built a deep bond with Byakuya and her appearance no longer mattered, so there is no need to keep the same hairstyle that Hisana has. When Rukia became Vice Captain, Byakuya calls her to his room and presents her a samite box. Rukia then opens the box to reveal a pair of white gloves made with silk, with the Kuchiki clan symbol sewn inside the glove. Rukia soon realized it was custom-made for her. Byakuya tells Rukia that after becoming a Vice Captain, chances of using zanpakuto will be frequent. Her zanpakuto is an ice type so wearing the gloves will prevent her from catching cold or frostbite very easily. Rukia can't help but to take a deep bow to express her gratitude towards Byakuya while holding her gloves.
The story also mentions that the reason Rukia is able to promoted to be a Vice captain is because of a recommendation from Byakuya. Also in one other part when Rukia finally found a way to regain Ichigo's power and went on to ask for help from all the team, she falls down carelessly, causing her nose to turn red. When she returns to the Kuchiki house, Byakuya noticed her red nose, yet he did not ask what happen. However, when Rukia returns to her room, Byakuya went straight to Hisana's altar, facing the portrait of Hisana and spoke softly: "should I ask what happened...?"