In New Moon, Rosalie explains to Bella that, when she was a human, her one wish in this world was to have a baby, which is why she's against Bella foregoing her ability to have children in order to become a vampire. When Bella calls her for support, because she fears that Edward will harm the baby to save her life, Rosalie becomes Bella's bodyguard.
The fierceness with which she protects the needs of Bella's baby (even when it's not clear yet as to its nature), causes Jacob to accuse her of sacrificing Bella's life for her own vicarious experience of having children. Yet, when Bella becomes a vampire, Rosalie is the first to push for Bella to hold Renesmee and to trust in Bella's control over her killer instincts when faced with her daughter.
To find out more about Rosalie and her problematic relationship with Bella, check out our entries on her in our guides to the other Twilight novels.