SirSpamalot,I am so sorry this is so tough at the moment.
I agree with Mopmay - really truly Please don't beat yourself up.
You said But 1 DC decided to stab another in the arm 'to see if it hurt' today, what was used, a pencil? Or something 'worse'? You do not need to answer that but if it was anything more serious than a pencil I do hope you will get some help to work on resolve whatever issues might be involved. Our son (now 4, adopted a year ago at 3) went through a phase of doing stuff like hitting my arm and asking me if it hurt. I was honest if it did or did not, told him not to do it and talked to post adoption support. I do wonder if working out whether things hurt or not is part of making sense of their own lives. But that is just a total guess!!
Re I'm not sure that there is anything I feel proud of. And that makes me feel utterly, utterly awful. Please, please do not feel bad. Recently, I was having a really tough time with our son, I was getting so fed up with the constant crying and complaints etc. I was picking him up from school and turning up late for him and feeling very resentful of his behaviour. One day the teacher said something about being late and I just started crying. Luckily my son did not see and me and the teacher got to sit down together and I explained things were rough. The fact that I could talk about it freely and she was so encouraging and reminded me I was doing a good job (which I think I am) really helped.
Re I know what you mean but I'm at a loss as to what to suggest to the school in terms of behaviour management. I think you need some professional help from post adoption support, this should not all be on you.
SirSpamalot, re Facebook, I also just wanted to say that I got my kids reports on Friday and did not read them for hours. My newly adopted son (one year in) seems to be coping well at school and my birth dd, very dyslexic is quite hard work at home and has never coped well at school.
I feel that when other people shout about their kids qualities or skills on line I just ignore, I try not to read them. You never really know what is going on in families. I know people who have birth kids but their are health issues with a child or have been with a parent or where a marriage has broken down leaving the single parent coping alone etc etc. For some of these families a 'good' school report will really be a reason to shout and celebrate. They are not doing it to make others feel bad.
Over many years I agonised over family photos with masses of kids from friends and on Facebook, because I could not post such photos as only had one child, and now I have two I can't post photos as one child is adopted!
But over the years I have learnt to let others chirp about what they like on line and not let it bother me; they don't have the same joys of sorrows I have with my kids but also I do not always know what has happened in their families either.
SirSpamalot can I tell you a bit about my situation and see if anything is of use to you?
With my dyslexic dd (who is 10 and is at least two years behind in school) we have done a few things that have helped me/her/us:
-Been in touch with a dyslexia charity for support and input (if there is ever a specific reason for your kids behaviour or difficulties with studies do seek any professional help you can, it makes a massive difference).
-I've kept in close touch with school, who have basically been pretty crap on the whole but where individual teachers have worked amazing hard for my dd. Some have been encouraging for me and generally spotted good things in my DD and told me, and have therefore shown me they do get it! - They were sometimes in the minority. 
With my relatively newly adopted son we have done a few things that have helped me/him/us:
-Been in touch with post adoption support, who have been brilliant. They do attachment work and really, really helped in the early days when things with our son and our birth dd were pretty tough.
-I've managed to maintain a good relationship with our son's class teacher who is a lovely woman and seems to know a lot about children... BUT I always maintain with both kids that I do understand my children more than the teachers do, and ultimately I made decisions like keeping my son back so he started part-time in term 2 and full-time in term 3 of reception.
Anyway, those are my thoughts for you, I have no idea if they will help but hope they will. 
PS TongueBiter, Re throwing tomatoes at break AND lunchtime, you'd think the school would keep the tomatoes under lock and key! It seems funny they mention the tomatoes when the stones would be more worrying.