Instead of extending "extra kindness" to her, focus on just being courteous. Courtesy is what people who work together owe each other. Your co-workers are under no obligation to like you. And you are under no obligation to like any of them. But you do have to be courteous and cooperate for the purpose of getting the work done.

Accept that you don't really like her and she doesn't really like you. That's okay. You're not married to her. She is just someone you have to work with.

Going around being "cool" toward a co-worker is not all that mature. Your relationship needs to be businesslike, neither warm nor cool.