YANBU I think you should send him to a holiday club. use that time to spend quality time with the other two children but also for you and your husband to jointly put a strategy in place for sorting out his behaviour. then when he returns, start the strategy.
If he is good as gold at school, then he can control his behaviour. he is therefore choosing to behave the way he does at home.
has he always been like this or did it start at a particular time or age? can you pinpoint when it started? maybe if you can pinpoint it, you can find the reason why he has become like this.
I think you need time out though. quality time with the other kids and also your husband I bet. Also talk to the other kids. ask them how it affects them.
also, let your son know how his behaviour affects you all and upsets you. dont shout or swear at him. just a calm mature conversation with him.
praise him when he is good but also let him learn that his bad behaviour means he will be the one who loses out ie he misses out on treats, he has to clean his mess and gets extra chores. have a behaviour chart with targets on so if his behaviour is good and he achieves targets , he gets a reward eg a special dinner, to choose a dvd to watch, a day out etc.
do also get professional advice though
best of luck