Hi G.. That would have driven me crazy and I probably would not have been patient or tolerant about handling that behavior.
Since your child is of the age to be finishing kindy or first grade, I'm going to assume that you homeschool. Homeschooling can be a great educational option, but it also may mean too much time together.
If she has so much time to complain, I'm wondering if she's bored and spending too much time at home? It may be time for dance class, gymnastics or an art class. Also, one of the benefits of home schooling means a less structured environment than the formal classroom setting, except that there are some children who need that structure. I'm not saying that you should opt for outside schooling instead, but to look at the structure of the day and determine if there is too much free time.
Being tolerant and kind about this annoying and sometimes rude behavior means that you are affirming to her that it's okay to behave this way. It's part of parenting to teach her that it's not. Also, I can't see what is happening in your house but if you are doing too much for her, it's time to teach her to solve her own problems. Teach her that when sister is getting on her nerves, rather than coming to you, she just needs to say that she's going to play in her room alone now. Complaining about the cup she got would have gotten my kids the response of "I guess you really don't need a drink right now. Go to your room til you are ready to apologize." But really, are you serving drinks to a six year old? She is more than capable of getting herself a cup of water, and therefore, picking out a cup. You're cold? I don't need to hear about it. Go to your room and get yourself a sweatshirt. If you are doing too much for her, she is seeing you as someone whose role it is to meet her every need and that she is the center of your universe. It's time to nip that behavior in the bud, Mom. Good luck.