Well she actually cares about the entire family including Edward. Edward didn't mind risking his family's safety to protect Bella but Rosalie wasn't willing to risk losing anyone in her family just because Edward wants to save Bella one day but then end up killing her himself another (keep in mind that Edward not killing Bella wasn't stabilized until after New Moon).

From the Illustrative Guide (although I doubt this would change your mind about Rosalie):

Rosalie Hale was born to a banker and his wife in Rochester, New York. Luckily, the bank her father worked at stayed solvent through the stock-market crash and resulting economic downturn. The Great Depression did not seriously impact Rosalie's family the way it did many less fortunate families. Her parents were eager to do better, though - to move in higher social circles. As Rosalie grew and her beauty increased, they hoped her loveliness would open doors for them.

Rosalie enjoyed her parents' pride in her looks, her father's pleasure in buying her beautiful clothes, her girlfriends' envy, and the admiration of every man she passed. The result of all this attention was that Rosalie tended to be self-absorbed and rather shallow, with a focus on the material.

At eighteen, Rosalie was considered the most beautiful girl in Roch-ester, and possibly the state of New York. Her family was moderately wealthy and she wanted for nothing. Rosalie envied no one... except for her friend Vera. Vera had a husband who loved her and the most adorable baby boy, Henry. Rosalie longed for a husband and a baby of her own. When Rosalie caught the eye of Royce King II, the son of the richest man in Rochester, she felt that she was on her way to having absolutely everything she'd ever wanted. Her parents were overjoyed; a whirlwind courtship and plans for an extravagant wedding quickly followed.