Oh, my. Yes, it is important to not encourage her whininess and to not give in to her temper tantrums. Sounds like you have your hands full. Maybe something like: "I do care about you. However, I am not going to listen to you if you use a whiny tone of voice?"

And if she starts a tantrum, then just start walking away--ignoring her. Embarrassing, but if you give in, then she will persist.

Sounds like she gets louder and louder to get your attention, as I say. "You can get as loud as you want to, but I am not going to listen to a loud tone of voice. If you speak to me quietly and respectfully, then I will listen....." And I wonder maybe if she does wake the baby, then you go tend to him--not saying anything to her about doing it. In fact, purposefully making sure not to pay attention to her, but ONLY to the baby, maybe saying only something like, "I am going to need to calm ( ) down and to try to get him back to sleep." And maybe "If he goes back to sleep, then I might be able to listen to what you want to tell me, if you are respectful about it"?