Just to preface, I did read all our your original posts and most of the response, but not all!
We have been experiencing all most all of what you have described with our ds (13). Here is what we have done...
Years of counselling, which helps some, but to be honest, only ever seems to be a short term fix. I think we are finally making some headway. His bio mother left him and dh when he was about 2 yrs old. According to several people, this has caused him to be "stuck" at that age emotionally. It is a form of trauma. Maybe the situation with your dd at age 3?
We were told to look at him as though he were a 2 yr old instead of 13... and wow! He acts just like our 2 yr old!
So, the answer was how do we get him past it. We have been doing EMDR (you can google it) during counselling sessions. It simulates REM sleep and helps people to process thru trauma more quickly.
We also started him on Fish oil and b vitamins, plus cut out dairy and gluten completely. It has helped alot with his impulse control and his associated stomach issues.
Lastly, and in my opinion, the most drastic, we took him to a homeopath. Her assessment of him was almost exactly the same as our counsellors... no impulse control, emotionally thinks like a 2 yr old, egocentric, prone to violence, attention defficit, and possible depression accompanied by mania.
She gave him a remedy and within two-three days he was a different kid. So far it has been a month and we have gone from 1-2 outbursts like you describe a DAY to ONE the entire month. FWIW, we have been dealing with these for YEARS. I can not tell you how great it is.
So, please do not think it is you, or your home, or anything else. We were told by people that we needed more structure, less structure, to put him in public school, get him in sports, take away the computer and TV (which we did do, but it didn't solve the problem~ It's still not back, but only because it is so much nicer
) medicate him, you name it. We went with what we felt was best for our son and our family. All the suggestions in the world don't make any difference if it isn't what you feel is best for her.
Good luck, and I feel your pain! Hang in there. We aren't through it yet, but there a light starting to peek thru.