i think you just need to be careful which instructor you use - if there is a choice of more than one class, go along to each one and see which class you feel most comfortable with. They will all tell you that children are told that they cannot use it outside, but some will be better in terms of reinforcing this than others!You will need to go with your instinct and aslo with whatever class you son feels most comfortable in. As for the hitting, I go through this with one of my kids, he was quite bad for it for a while, more in a pesty way than particularly aggressive - the school thought that it was because he was shy and trying to get attention. Have of me thinks it has merit the other half thinks what a lot of rot!
So, we have gone for a two pronged approach of trying to equip him with the skills to socialise more easily, telling him disappointed we are when he hits someone and frightening the living daylights out of him with what might happen if he keeps on hitting - luckily, our neighbours daughter has had a recent encounter with a boy that hit her (maybe not lucky for her though) my neighbour callled the police, and I was able to tell my kids that the reason for the police being round. i.e. if you hit someone, their parents may get the police round.
having said that, he seems a lot better - but we need to watch what he drinks as any kind of squash seems to make him more aggressive.