Hello... welcome to Just Answer.
Are your daughters actually hitting each other or is it more verbal?
Sibling rivalry is normal. Your daughters need to learn how to negotiate, problem solve, and cooperate ...but these skills must be taught. If the put downs continue, tell them that we are using kind words about each other and doing kind things for each other. If they do not follow through, make sure that they know beforehand what the consequences will be. When you hear them talking about each other, set them aside and have them role play the correct ways to speak to each other. You can even participate as a model of what types of behavior you would like them to exhibit. The sibling rivalry is an issue that you must constantly stay on top of or else it will progressively worsen. Also, make sure that you are not showing favoritism toward a particular daughter. Additionally, make sure you as the parent are not screaming and yelling yourself at your daughters when they are "fighting".
If this has helped, please ACCEPT. Have a great day!!!