Your son's behavior is obviously causing a lot of conflict at home. Because Aspies really do think differently than "typical" people, it can be difficult for parents to understand what we need, and the younger Aspie's do not have the words to explain it. And sometimes even when we can articulate our needs, it sounds dumb to "typical" people and they won't allow it.
As an adult with Asperger's, I find that I can "pass for normal" in most social situations. It's a chore, and creates lots of internal stress. As soon as the situation is over, I frequently have a meltdown. Sometimes I leave early because I can feel that I am about to "lose it", but the other people will never know. This could mean when I get in my car, to the bathroom, home or a good friend's house, or wherever I am where I finally feel "safe to be me". My meltdowns will subside within 30 minutes or less, but for that time period, I need to be able to do EXACTLY what I want to do. If it's go somewhere private and cry, read, close my eyes, scream, hit a bat on the bed, talk, not talk, or cry on someone's shoulder. This is my way to release the build-up of stress.
It sounds like your son is "coping" at school, but then breaking down when he gets home. With my son, also an Aspie, I set some ground rules while he was coping well, then always followed through on them. I tried to give him more control over his life and choices from a young age. There are things worth demanding, controlling, and fighting over, but most things aren't. There are certain things he HAD to do. Like immediately obey me when we are out in public (mostly a safety issue, stay by my side, cars might hit you, someone may try to take you home, mom won't be able to find you, etc.). You can be messy in this room, but not these rooms. As a teen, a new rule - you must have clean hair before going anywhere with me. If he didn't and wanted to go somewhere, tough. (I wish my parents had set this rule with me! I can still remember the stringy, greasy mess of hair I'd go to school with, but my parents had more severe problems to deal with than my dirty hair.)
Think about it this way. At school he is always doing what someone else tells him to do. At home, if a parent is always asking questions, telling him what to do, he is again doing what someone else want him to do. When does he get time to do what HE wants to do? We need lots of hours doing what WE want to do because it gives us pleasure, makes us happy, and calms us down, and makes us "play nice" with others
. Doing what other people tell us to do gets us very stressed, especially if we don't agree with it.
We kind of stay in the "terrible twos" all our lives, want to do it MY way, not your way. As we get older we learn how to say no and make it stick. Some of us learn to do it without causing conflict, some don't. While we are younger, we can be a pill for the adults who need to teach us how to live and fit in the world. (interpretation - "act like a typical person" because it's not ok to be who we are.)
Think of the situations when your son has the behavior problems. Is he still trying to calm down from school or other social situations, and he's told to stop his stemming or strings or lining up cars or spinning to do something for someone else? Does he get more upset when he is not allowed to do these things that calm him down? WHY does he freak out in the bath? Sometimes if the parent knows why the child is doing the behavior, what the trigger is, they can find other ways to get the need met. Try this exercise - try to pretend you are him, and write down what he would say if HE were writing on this board. When the WHY behind the behavior is understood, the solution will sometimes be obvious.
Perhaps he needs sent to his (quiet) room to play alone for 30 minutes when he gets home from school. When I worked, I would go straight home from work and lock myself in my room. (Come to think if it, I did it when I was in school, too.) I needed the 30-60 minutes to calm down before I could go pick my son up from daycare. At work everyone else demanded my time, then my son demanded it once I got home. I had no time for doing my calming things, and felt constantly overwhelmed.
Just trying to give some insight into the inner workings of an Aspie, in hopes it will provide some clues as to what may be going on in your own son's head. Good luck.