I wish you the best of luck in this endeavor. I'm currently enduring the same ride in the kiddyland, here. My daughter is 8 and disagreeable, argumentative, and moody. My mom's theory is that they are maturing faster because of all of the hormones in our food, so they are starting to hit the pre-PMS stage earlier. I have to say that there are days I would like to try to give her a Midol and see if it works. ;)
My best advice is to be patient. Try not to overreact to her rants and tirades. Be straightforward with her and when she starts to go off, take advantage of her bedroom. Send her to it. If she can't hear you over her own voice, then you are getting nowhere. I treat a tantrum or breakdown just like I would when she was 2, I send her to her room until she is ready to calm down and talk civily to me about what is bothering her. I have 2 younger kids (both boys, almost 4 years and almost 9 months). My daughter knows they need attention but it doesn't stop her all of the time.
One thing that has helped is setting aside (never a set time) some time to ask her during the day how her day has been, what the best part of her day was (or the day before depending on when we talk), and just finding time to actually let her tell me what is going on in her life in a positive way. Also, I'm part of a book club. She loved that idea. So she asked me to be part of a Mommy and Daughter book club that included just me and her. She picks a book for us to read (so far she's picked ones I've already read) and then we talk about it after she has read it. It is great and opens us up to conversations on some topics we wouldn't have considered otherwise. We, also, sometimes talk about what her brothers are doing and what she thinks about it. Like our 3 year olds potty training a few months back and his looking forward to starting preschool in the fall or our almost 9 month old's attempts to talk and walk.
I have to say that being patient and trying to listen to her actual complaints and accomplishments when she is talking to me calmly does help. As for all of the fight and moodiness, I have 2 younger sisters (now grown) and 3 young cousins that my parents are now raising and I know that this time in their lives will pass. It does take a while. My mom said, that first they realize that you don't know everything, then for a few years you get dumber and dumber, but somewhere down the line you start getting smarter again. It is at this point that you actually develop a better relationship and can become more than mother and daughter. My mom's been through it 3 times and I think of her as a wonderful asset and friend, so in this I believe she is fairly correct.
Knowing this from her experience, I persevere. I chant my mantra "This will pass, this will pass, this will pass." (I chant this silently to myself a LOT. My almost 4 year old has hit the why stage recently. Only with him, it is not just why. It is why, who, when, where, what and how. ;) ) The hardest part is not losing patience or hope that we will get past some of the behaviors and antics. I wish you luck with your daughters. Also, if you ever want to rant or commisserate please feel free to email me.