Hi! I am a parent; I also work in schools with special needs kids, including those with behavioural issues and I know that this is all too common. There are two sets of practical/political problems in such a case:
1. Usually, the bad behaviour is not going to change, certainly not in a hurry. The school cannot wave a magic wand and fix it immediately even if all staff were brilliant at all times. The underlying problems in these kids' home lives, in their neighbourhoods, in society etc are too great. Any progress at all is necessarily slow and the well behaved kids suffer.
2. Most schools' governors and heads are under tremendous pressure - from everybody from the Prime Minister down to the local councillor and borough officer - to keep a lid on things, keep kids off the streets and somehow claim that standards are rising according to GCSE and A level statistics. Dare I say it: that any member of staff who challenges this will be ignored, stamped on or end up in severe career trouble? And the full resources needed are rarely availalbe in any case. Class teachers and teaching assistants are often in an impossible position and are desperate to be supported by their seniors . Exclusion is not nice, the process takes for ever and it counts aginst the governors and head. ( There is also conscience. I know one head, an admirable man, who is adamant that as an educationalist and a man of conscience, he will never exclude anyone again.)
So, do follow the suggestions already posted. Also, write to the Chair of Governors and remind all about the law of 'inclusion'; i.e. that all kids' interests should be looked after. And what does the school's policy manual say? What is it committed to providing to each child, perhaps as part of its contract with pupils and parents? The school web site should help or you can ask for all the policy manuals. Same
for the Borough's policies.
You may also want to mention, at some stage, that you are reluctant to write to the Borough Chief Executive or the Council Leader or to take legal action. You will also benefit from acting in a group if this is possible - chances are that many other families are similarly frustrated. Yes this will not make you popular and they are relying on you giving up sooner or later. This is a political problem and you will only win by exerting both subtle and crude political pressure on all these individuals. Remember, you are the customer and the citizen and the parent and the taxpayer. They all work for you. (What do your own Councillor and MP have to say, by the way?)
This is really a horrible position to be in. But, with persistence and following the suggestions so far, you will eventually get somewhere and probably earn the sneaking regard of the school. Good luck!
Finally, there are many issues we could all get worked up about here, and rightly so. But I hope that, at least on this thread, we stick to helping this one pupil and others in a similar position.