try talking with her what going on in her mind why is she jealous with her younger sister . does everybody in house give more attencion to the younger one so may be she is not liking that . or may be she getting insecure that why she is rude to other . try giving her some confidence so that she does n feel insecure . try doing this may this help her and you.
All the best .
Make sure your daughter is getting a lot of attention, and is a big part of caring for her younger sister. She needs to feel needed and loved. When kids want attention they will take bad attention to none at all. It's easy to get caught up in caring for a baby when you have one that is pretty independent, but her jealousy may stem from not feeling a part of it all. Talk to her about being the big sister, and how her little sister needs her to teach her things and play with her. Plan days for just you and her to do something special together, something she really wants to do. Praise her when she acts like a "big girl" and tell her how smart she is and how her little sister needs her help every day. Once she sees that she can actually help her little sister, and interact a lot with her, they will bond. Always make sure she gets as much attention as the baby. I do think her jealousy is playing a big part in all this. Good luck and take care.