This sounds just like my (almost) 4 year old son. He has times when something very minor just sets him into a screaming, shaking, uncontrolled fit. Sometimes they last quite long. The last one was 1 1/2 hours. Luckily they aren't frequent.

We only have one child. He has CAH SW. I don't have any non CAH children so without a comparison, I can't say if his tantrums are CAH related or not. But,  I do know they are related to sleep and hunger. I am getting much better at recognizing the build-up in intensity - he is almost like water starting to simmer. When I see the triggers I jump in and be sure to keep his environment calm and moving in the direction of sleep or food, whichever time of the day it is. This really seems to help.

Just tonight he was starting to lose it. It was 7:00, he is out of naps now, he was up at 6:00am and we had a busy day. He was mad at a very little thing and kind of threw one of his toys across the room (A huge no-no in our house) and I knew we were headed for a big one.

We had a very similar situation last week and that time I stuck with my standard discipline of explaining and then taking away the toy in question. Well he just lost it. (That was the 1 1/2 tantrum I referred to). He was completely unable to control his emotions.

This time I tried a different response. Rather than taking away the toy in question I just guided him into a different room; I still did the explanation part but not the toy removal. Instead I started prepping him for bed. He was asleep within minutes. I am sure he was just so tired he had no emotional control left. 

Is your  daughter out of naps? If so, maybe this is why afternoons are hardest for her. Especially if she has been holding it together all day while she is with others, it may be natural for her to lose it when she finally can in the afternoon. Just some thoughts. I hope this helps.