The Princess and the Pirate by Felicity Banks

Princess Ana is trapped in her own home, unable to leave the castle walls to avoid a fever that is plaguing Ratu Island. Her mother, devastated after the death of Ana's father, has hardened, resolving to keep her crown rather than acquiesce the kingdom to her son. The only person who might be able to change the queen's mind is Ana's grandmother, Sol - who just happens to be a murderous pirate. Ana's beloved Auntie Livina hatches a plan to send Ana to seek out Sol, while also keeping her out of reach of the deadly fever. Ana is thrilled for her newfound freedom, but terrified about meeting her grandmother. What if she's beyond reform? What if she tries to kill Ana?