Dear Orange,
it sounds like the battles are...well, how should I put it. Yours? I was going through this with my DS until he was about 5. Our home turned into constant battle ground, from early morning on, he would be demanding, me resisting, him defiant, or I would be demanding, him, resistant, just constantly. Then I realised the problem was really not him. It was me. I wanted him under control, make my life most comfortable and stopped seeing him as a small person with complex emotions and lack of knowledge. As a result, in my defiance, resistance, demands I turned into an equal with him -- into a five year old. I could not carry on like this. I was just constantly feeling I am unable to keep my patience, I was unable to function with him, I frequently did not want to have him near me. It had to stop, and I had to change my whole way with him.
I was helped in realising my problem by a few books that changed my whole approach. I can see the books you have been using are of a particular type, i.e. emphasising the same pattern where the mother is the one who has to be in control, and the authors are giving them tools or justifications how to gain that control. It is worth recognising that rewards are just the same as punishments in that they belong to an authoritative, controlling kind of parenting. I suggest you look at one very helpful book "Helping young children flourish" by Aletha Solter (if you do not mind reading, there are also books by Thomas Gordon which have helped many, and there might be Parent Effectiveness Training opportunities available www.gordontraining.co.uk/ where you live.)
I found the approach offered by Solter very liberating and it has, slowly, started to mend our relationship. There is less defiance, less resistance, more cooperation -- but perhaps more importantly to start off with, it has freed me from this need to constantly control him, through a daily, excruciating battle. It really eats one's soul, I can so relate to your desperation.
It helps to to take a step back and start thinking differently. It does not mean you stop setting limits: on the contrary, I do so now much more efficiently. I set the requirements clearly and in a friendly manner. If he protests, I listen to his reasoning, if he offers any, and if it makes sense, we can reach a compromise. But if it is something that cannot be argued with, I do not try to stop his protests. They are only natural - wouldn't you protest when stopped from doing something or expected to do something you did not really want to? It is completely fine and even healthy that they protest. But instead of walking away or admonishing her for protesting, you can accept her feelings by being there, if she lets you hold her, offer her your compassionate embrace. You will find that over time she will learn to express her emotions in a more acceptable way and that there will be less standoffs as she feels safe to be emotional with you. THis is what I am now starting to see. It has taken a few months, but to be honest, the way you are describing your current life, it looks like it leads to simply worse standoffs and, in the future, a broken, unhealthy relationship.
Good luck!
M