Hi,
Reading through all your posts, OP,this might be the best link for you and then you can choose between them
www.ahaparenting.com/parenting-tools/Discipline
As there seems to be a sort of escalation of behaviour with your daughter , I wonder whether it might be worth you investing in a coaching session with laura markham - she's based in the US but does Skying...
( To keep me going! I get her regular emails and use her site and refer to my 3 fave parenting books - UP alfie kohn, how to talk, and peaceful parent, laura markham)
Have done a long postings to give you some of our real life examples....to your question what else can we do instead of punishments and rewards? there really are lots of things.
The reason I would encourage you not to give up is that me and DP are really in quite a minority in the way we parent -and DS1's primary school is full of liberals! - so we're encouraging anyone else who's trying as well cos it's tougher in the beginning.... It hasn't been plain sailing for us , especially when DS1 had the dreaded testosterone increase age 4 when DS2 was 4 months old.
I use a lot of stuff from laura markham's book. E.g. we have weekly family meetings ( v quick of course about 20 mins max ! - we started them when DS1 was 6 1/2 and as DS2 was just under 3, we used to say we're just having a family meeting - join in if you want to but we understand if you just want to play. But he did join in!
Both boys give their choices for the weekly food shop and really feel that their opinions are taken into account just from this small step of getting chicken legs instead of chicken breasts, and about 2 months ago, when we got to the end with AOB, DS2 age 3 said "oh yes daddy, we need a new light for the upstairs loo!"
Because neither of us were brought up this way, a lot of the stuff seemed unnatural and I have been on quite a journey and continue on this journey.....
We have kept going through the sort of difficult times that you're experiencing now by keeping the long term relationship with our children in mind.
It is an amazing experience to see our 2 children learning to emotionally regulate themselves ( DS1 stopping himself thumping DS 2 by saying, when you snatched my toy away, I was really irritated, lets think about what the options are) be thoughtful ( when our washing machine broke a few weeks ago, and I was getting stressed about it DS2 came and gave me a hug and said" you seem frustrated, but don't worry i'll help you calm yourself down, let's call someone to fix it!!!!) ,to hear things about DS1 at his parents' evening like - he gets on with everyone, his problem solving abilities are extremely well developed for his age etc etc.
Wishing you lots of luck - I would really like to hear how you're going in a few months so please think about PMing me in a few months time...