I've heard two different explanations for this. The first is that the child has to expend so much energy keeping it together that by the time they get home they just fall apart. The opposite is that school has more structure and home is too chaotic.

I don't believe in blanket explanations because our kids are individuals and their situations are all different. Try to get the school to partner with you in figuring this out. It will require analyzing both the school and home environments. A qualified behavior analyst is the best person to do this.

At 18 my son is now able to explain some of these things to me. He has told me that he is exhausted by the effort to navigate the school day and finds it harder to keep it up at home without some down time. He hates confrontation of any kind so he expends a lot of energy trying to do what is expected of him at school. I think the kids who are better at this probably show the most difference in behavior between home and school. They bottle up all of the frustration until they reach their safe zone. I try to give him his space for a while after he gets home from school.

When I ask him why he is so cooperative and polite to others but less so with me he tells me it's because I am family and he can be that way with me. Somewhere along the line in his efforts to understand social rules he has categorized people and responds and acts with them the way he has learned. There is no grey area for him here. He either has to be polite to you or he doesn't. I'm in the doesn't column for being polite to and listening to as far as I can tell. He laughs when I tell him he needs to be polite to his parents. I think that is where teachers may see an entirely different child at school from the one we see at home. I can tell him something and he refuses to listen but if the teacher tells him the same thing he will. Of course some of this is just teen behavior. He's reached the age where mom is not all-knowing. sigh.....

I wonder if your daughter isn't coming home exhausted from the effort she extends all day trying to "fit in" and to look like everyone else. We lived in Italy for three years; those days that I was out in the community a great deal really wore me out. Everything was a thought process: how to get somewhere in crazy traffic, how to ask for what I wanted, converting liters of gasoline and continually figuring the money at the current exchange rate.
My own experience with the school (just our school, just our children, not a sweeping statement of truth here) was that the school is set up for typically developing people. Those outside the parameter have a tough time. Bureauracies tend to take care of themselves, in my experience, so I wasn't always convinced that everything was as rosy as I was being told.
So, when our small folks got off the bus we watched a couple of shows together, whatever the favorite was at the time, and had some popcorn. The space seemed to help avoid the explosions that were inevitable after all day of trying to be something they were not. We were, sometimes, even able to talk about some portion of the day.
Good luck. It sure is a difficult experience all the way around.

I am in the exact same position. My son is 9. He is usually the best behaved child in the classroom. He follows rules to a T. He can not understand why other children would break rules. Right after school, however, he often has meltdowns about something that happened at school. He stays on grade level unless there were timed tests involved. At home we have frequent "out of control" moments displayed through anger or crying outbursts. It is exhausing!!!

My 16 year old son keeps it together at school and exhibits what I call a "drunk like" behavior at home. Very obnoxious behaviors to my wife and I in the evenings and the mornings before school. At "back to school night" I wonder if I'm in the wrong room because the kid they are talking about doesn't sound like the kid I have at home. Afternoon meds don't seem to be helpful. Also tends to have trouble going to sleep at night and staying asleep as he tends to keep wanting to go to the bathroom.