OK, rather than prejudge, I am going to tell you what happened today.
DD1 and DD2 (2.5) and I go after school to the park to walk a friend's dog. Dog is young and lively and friend continually tells DD1 not to throw things at or near him, to approach him from the side and not the front. DD1 ignores this repeatedly, despite my reinforcing it. DD1 asks to go to playground, I say no. Shortly after she bolts - running quite some distance and not responding to "stop" or to her name. We leave straightaway and do not go to playground. I tell her off in the car on the way home, and once home I tell her (in consultation with DP) that there will be no TV today. She doesn't seem that bothered.
Later, I try to talk to her about what will happen next. I ask her to listen, which she does briefly, before continually fiddling, turning away etc. I explain very clearly and briefly that for the rest of the week I want her to listen, and to do as I ask, and then, if I am happy with how she has behaved, then she might be allowed to help friend walk dog at the end of the week. When I asked her to tell me what I had just said, she told me something totally different. Her response to breaking rules is to say "I didn't remember", and to us trying to explain stuff is "stop talking".
I am at my wits end - I spend half my life trying to catch her attention, and the other half trying to stop her doing something that she shouldn't. Needless to say, a lot of our interactions with her are negative.
I give this example as a concise version of how she is and how I respond (in this instance, calm, clear consequence, follow through, try to build towards better behaviour). But she just cannot grasp rules, boundaries, and certainly cannot apply them herself.
She is in Junior Infants (reception), and seemingly doing well there, although I suspect she is struggling socially. Academically she is fine, but I think not working anything like to her potential - she is easily distracted, tunes out, acts silly. But we are getting to the point where her behaviour, or inability to follow clear, basic rules is impacting on our capacity to do things as a family, and is certainly placing strain on other members of the family.