I found this book very helpful
http://shop.nogreaterjoy.org/to-train-up-a-child-bookWarning, like every book you must take what you want and leave the rest. Its also Christian based, but can apply to all families.
Everyone talks about the terrible 2's but I'd take 4 two year old over a 3 year old. My son and stepdaughter both went through a stage at 3.
Consistency is the thing. If you say your going to do something(take something away, not go somewheres, etc.) No matter how much she screams, yells, fusses, don't give in. If you do it once she will test you every time. If you have already done this, be prepared, it will get worse before it gets better. She will keep kicking it up a notch to see if it will work. I use to put him in time out and if he screamed and yelled, he got to stay there longer. In the end she's trying to break you, if she wakes up her sister, she stays there longer. Only once she is sitting nice and quiet, and YOU or your husband come in to talk to her, is she allowed to apologize and leave. Wesley fought against me for well over 3 hours the first time I tried this. he landed up falling asleep. And every time the time got shorter and shorter. Now I just mention time out and he straightens up.
I know you feel like your relationship is suffering, and I know myself I felt worse when I was coming down hard on Wesley, but when he got into line our relationship improved. At the end of the day though, she is your child and not your friend. I agree with you though, you should not have to reward her just for her to behave for you.
I found that when I was having issues with Wesley getting up for school in the morning, I created a check list of stuff that was expected of him. If he did everything without fuss and wasting time, there lands up being a bit of time before school for TV, if not there is no TV time. I don't tell him, "Oh if you hurry, you can watch TV." I just turn it on when he's done, or if he has been stalling I don't put it on. But the check list of stuff that is expected of him helped us soooooo much!
Also if she is still playing the ill card, what I did with my son was tell him he needs to rest if he is so ill and then I would pull out a rare treat for me and hubby to snack on in front of him.(The most effective if we were out was going and grabbing fries from McDonald Drive through) Of course suddenly he was better. But it didn't matter, he still did not get any, because liars don't get special treats. Of course the first few times he screamed and yelled, but after we got though that, he stopped using that as an excuse.
I know I must sound harsh, but I know with my kiddo if I'm not, he runs wild. If I'm strict when their is behavior and loving when he's behaved, life is much better.
Good Luck with things. Each child is different, so I'm sure so you will find what works best for you. Just remember its TOTALLY normal for things to get worse before they get better.