A swc is hard to parent. For starters.... pick your battles. Decide what is really important to you and stick to your guns over that. The less important things can go. My swc refused to wear a coat at that age.... I couldn't battle with that... so she didn't wear a coat and sometimes other parents criticised me for that. However, she had to go to bed on time.... so that was worth the battle.
She used to take her clothes off all the time. If we were with people I knew and felt safe with, I let her. She doesn't do it now!
I had to ignore some behaviour (eg at 4 she wrote sex all over her arm, twice.... I ignored it and ask her pre-school supervisors to do the same. She got absolutely no response... and stopped. Had I responded, she would have continued to do it.)
The things that are important, you have to stand your ground, whatever happens. And try to stay calm. If you allow their behaviour to make you angry or stressed, they have won.
Smacking won't work long term. I don't recommend it.
We had problems with our swc being violent to her older siblings.... my hubby tried smacking and it had no effect.... it was alos a negative example to set.
My advice.... praise good behaviour whenever you see it, don't let them see you get stressed. Other parents can worry about trivia.... with a swc, you just have to pick your battles, or you will be exhausted and the child will feel disturbed as he/she will find no boundaries.
Maybe warn him before that he has to do what he is told when in public...explain why, then give a consequence... eg... we will come home from the park, you won't get a treat in the shop etc.It doesn't matter if he gets cross when he doesn't get his own way... many adults feel like getting cross when they don't get their own way... we just have to learn to deal with it, and this is what your son is learning, that he can't always have his own way and that it isn't the end of the world. Allow him to have some choice in his life though...Try time out for answering back....?

My swc is now a model school child, who although she stil has the capacity for single-mindedness, has learned to direct her energies. She is doing really well and isn't a bully (which was my fear when she pushed other children around when she was little.Don't worry too much... just stand firm