Oh babe. Hard work eh? Poor you. Personally I would put money on this being nothing to do with your daughter's attitude or Tracy Beaker or an early rush of teenage hormones and certainly not your parenting. I think it is fair and square down to the arrival of a gorgeous new baby.
My best guess on this is that your bigger daughter is using any means she can to wrestle attention away from the newbie. It actually makes perfect sense for her to be behaving like this right now, if you think about it. All Eliza has to do (unless she is a very unusual baby) to get you, your partner or maybe both to rush to her side day or night is look cute, gurgle, cry or poo in her pants. An 8 year old just can't directly compete with that, especially when you are most probably knackered because new babies though wonderful, are exhausting. However, your daughter is a clever and emotionally intelligent kid. She wants to know that in this time of adjustment and transition she matters to you and your partner just as much (and preferably more) than this new interloper. Intellectually she probably understands that babies necessarily take up time and energy and hears your reassurances that you love her as much as ever. She probably also thinks her sister is rather fab in many ways. But emotionally she's not prepared to accept this huge change in her world order without testing you to the limit and she's having a classic reaction to the new arrival. Think toddler dethroning in an intelligent 8 year old. Essentially she is screaming "I'm your first and most important baby!" at you as loud, often and unignorably as possible. She's too old and dignified to do this in the form of a complete toddler meltdown so she has settled upon being cheeky, needling you, arguing, behaving unacceptably etc. This is ensuring that your attention temporarily focuses exclusively on her. Even though she is probably sorry to upset you, she knows at some level that by doing so she is uppermost in your heart and mind at that moment and that is what she wants. Even if your thoughts about her are worried and angry ones that is better than the possibility that you are thinking exclusively of the baby instead.
I think that your daughter's behaviour is totally, utterly, annoyingly, maddeningly, wonderfully normal, tinks. I really do. And you sound like you are dealing with it just fine. There are no magic wands here. In time your daughter will adjust to this big change in her life and her behaviour will improve. In the mean time you just need to carry on doing what you're doing, I reckon. Try and give your daughter as much positive attention as humanly possible but be realistic- the baby needs you and there is no point in not acknowledging that. But if you can make some time when you and her can be alone without the baby and enlist special people in her life to spend time with her too- would this be a good time for her to have some special time with her nan or your partner, for instance?- I think that would help. Don't let her away with bad behaviour but try not to give it too much attention because I really think that plays into her hands. Keep letting her know that you love her loads and understand that this isn't an easy time for her but also let her know that you are very confident that things will settle down in time because she's a great kid and a great sister. Have you got any stories about your siblings? I can't remember where you come in your family but she might like to know what your memories are of any younger siblings coming along, especially if you see any parallels. My boys love hearing about how jealous I was when my little sister was born! Again, your mum might be able to help with that?
Anyway, hope some of this helps. You guys are a lovely family and this will pass. Honestly.