Sorry for clickbait title - bear with me because I promise I'm not that horror parent who believes their child can do no wrong.
Anyway. DS2 is 4.5yo. We live in Germany so he's still at nursery (kindergarten), not school yet. I actually couldn't imagine him in school (August birthday, so would be young in the year anyway).
We've been getting reports for a few months that they are finding him difficult to manage. It's mostly around situations where he is asked to stop doing something, if he doesn't want to stop then he just develops this selective deafness and pretends nobody is speaking. It's irritating - he does it occasionally at home, and honestly, sometimes we get irritated and shout in response. When we manage to stay calmer then we would go in and interrupt or physically stop the behaviour (e.g. if he was annoying his brother) and/or remove him from the situation. We would then tell him not to do it and reiterate that he had been asked not to (DH uses the word naughty, I prefer to give a short explanation of why e.g. "That will damage the wall/DS3 doesn't like that") Usually this is fine and effective, sometimes he will retort back with something like "No it doesn't!" which I think is quite normal for four.
If the behaviour continues or argument escalates, then I would look more directly into prevention e.g. take the toy that is being used inappropriately away, suggest a different activity, do some problem solving esp between him and DS3 (1.5yo) if they are clashing over a toy or something.
Or DH is more likely to give a warning that he would be sent to bedroom (this is literally next door so is basically time out)/to sit on sofa/TV turned off. After this he would then talk to DS calmly and ensure that he understood the reason for the consequence.
Although I've described these as my vs DH's approach, DH does sometimes use my approach - mostly removing the problem item or suggesting something else or distracting DS3 away, I will do the warning/punishment occasionally but I prefer not to, because I find when punishment gets involved it just tends to increase his tendency to be argumentative/wind me up back and it starts off a whole spiral which is ultimately unhelpful.
It happens more when he is tired/needs a poo/hungry/etc so when there is a pattern of him being especially nuts we would generally try to get a snack/meal into him ASAP or insist that he goes to the toilet, and try to keep on top of these things in general, which does help. I also suspect he is a bit sensitive to noise and he does not like being in crowds of rowdy people, which might be behind the fact that it seems to happen more often at nursery.
When he is in one of these "discomfort" states he is also likely to freak out and lash out (hit/scream/fall to the floor crying) over the slightest misunderstanding as well (e.g. if you unzip his coat when he wanted to do it, if the biscuit breaks in half, if his brother sits in "his" chair etc) although we aren't really getting reports of this from nursery, at least not towards the staff, they do say that he will lash out "randomly" at other kids. I don't think it's totally random, but I can see that it might be happening with very little provocation or seemingly with no provocation, because quite frequently he'll mention some incident where another child has "done something bad to me" or "did owie me" or even stuff like "I don't like those bad boys" but when you press for details he insists that he can't remember or he doesn't know, or he changes the subject. If you ask whether he told the teacher it's always no, they never know anything about it if you ask them directly, and stuff like when he was potty training he would have accidents and we'd say well did you tell the teacher that you needed to go to the toilet, and he'd say no. Sometimes I'd turn up to get him and he'd be wet because he'd not told anybody he'd wet himself. So my assumption is that he's getting into a disagreement of some kind (which might well be his fault, I'm not meaning that he's some put upon victim!) and, lacking the skills to deal with it maturely but also lacking the inclination to ask an adult for help.
German/nursery approach to behaviour/boundaries is like our initial response - talk to child calmly about their behaviour, they don't really do time out/punishments etc (though sometimes they will separate children into different rooms or take them elsewhere to calm down).
But anyway - here's the thing I'm finding strange. They report that this is happening approx 3-4 times every day, and that he is the child who is taking up the most teacher time. Apparently, the other children stop when asked to stop from the opposite side of the room/playground. I think that's unusual at four. (The children are age 2-6). I think DS is a bit stubborn but basically totally normal and even fairly easy - you can generally reason with him as long as you catch it early enough and he hasn't dug his heels in. I can see, as I've been writing this out, that it's quite possibly the "random lashing out" at other children which might be more of the 3-4 issues per day. Because this doesn't really happen at home, I hadn't really connected this, until I'd written it out here. I'd kind of written this off as just children squabbling.
But isn't this fairly usual for this age? I know that the lashing out is a problem. DH has already spoken to the teacher twice (and thinks that we need to be a bit more on top of consequences at home) and we have spoken to DS2 but it hasn't really helped. I do not want to do punishment at home if he gets into trouble at school because he's four and I think that's totally unhelpful, whatever response needs to be at the time (DH agrees). I am going to speak to them next week because I think we need to look at what's leading up to it and not just focus on the response. I guess I'm just a bit puzzled because I would have thought that the selective deafness and disagreements between children turning physical were quite normal behaviour for this age. Yes, it's misbehaviour, yes it needs correcting, but him being the worst/taking up most of their time really surprises me.
But maybe my perception is wrong? I just remember DS1 at this age being literally constantly in that hair trigger screaming dervish mode, not being able to cope with stuff like me turning off the TV, he wouldn't let me talk to other adults because he would be constantly running at me and being disruptive, and it wasn't happening 3-4 times a day but more like 10+ times a day. He was also a perfect angel at nursery and never caused any issues at all 
He has ADHD, explaining the extreme home behaviour, though I didn't know that until years later. And so do I, so it's not completely insane to wonder if DS2 has it as well although he is so much calmer that I had kind of dismissed this.