She is good at nursery, but is often very tricky at home. Mostly this is defiance and disobedience, which is annoying but manageable. But we are having a lot of 'stupid' directed at us when she gets told off, plus a good bit of lashing out physically. The sanction for this is time out, but this doesn't really seem to stop her. I am worried that we are not in control of her and can't really work out to establish control. Rewards, incentives, positive praise etc etc all work for a while, but nothing seems to work long term. She reacts very badly to being disciplined, and generally with try to change the subject, avoid eye contact etc if you try to talk to her about h behaviour calmly. She is very hard work, and I feel like I am not parenting her very well. This has been going on since she was about 2 and a half, and things are better, but progress is very slow. Dd has one sister who is 18 months old, and is doing fine developmentally as far as I know.
She craves attention all the time, never seems to learn rules, is impulsive. She hasn't really developed empathy very much yet. She is also very loving, sensitive, funny, highly creative, good at arguing (!) and we try very hard to focus on the positive, but this isn't always possible when she is pushing her sister or chasing the cat.
my view, am not an expert, just an experienced Mum with the benefit of hindsight .... you can't control them or be in control, but you can lay ground rules and help them understand what is acceptable and what isn't. On the positive side, your DD sounds like a great character, very strong willed, and very bright... which one day will stand her in good stead, if and only if she is shown where to draw the line now. You say time out doesn't stop her... then perhaps the time out isn't long enough or implemented strictly enough? (not a criticism, just a question).
I came to the conclusion that sometimes they need a way to back down from their bad behaviour whilst keeping face ifykwim. What used to work for my DCs was to say "I don't like this horrible (jane).. I want my lovely (jane) back... let's send the horrible one upstairs and see if the nice one comes back"... if the "nice one"came back, then I let it go. If not, the horrible one got sent back upstairs again. Might meet with disapproval from some but it worked for me (and gets a few smiles when I try it with my now teens)!