Challenging behaviour

My SS has been displaying some challenging behaviour for a while now, he's 6. He doesn't like to be told no, or to stop doing something, and when it does happen, he gets into a bad mood that can last hours. For instance, the last weekend he was with us, he'd just eaten a substantial lunch, and he instantly asked for snacks, we told him to wait a but longer for his lunch to go down and have some water, he became moody. Another instance is when he wanted a toy our two year old had, we told him he couldn't just have it and would have to wait until he'd finished playing with it and find something else to play with in the meantime, he got into a mood. Having a mood doesn't sound so bad, BUT, he will spend that time being quite horrible to us all. He will hit us, throw things at us, stare at us, do things like stand or lay in the doorway when one of us tries to walk through it, kick the sofa if we're sat on it, put his hand over the buttons on thr washing machine if we're trying to put it on, kick out belongings across the room. He's not out of control though, he's not shouting or raging, he's doing this stuff with a smirk on his face a lot of the time. However, he becomes more unregulated if we ask him to go to his bedroom to have a think/calm down, mostly because we don't want our son seeing the behaviour and mimicking. He's caused injuries to our son now too, he pushed him over which left a bruise on his arm and shut the door on his fingers which caused a broken fingernail. I'm nervous when he's around and refuse to leave them together ever, even to pop to the loo. It feels like walking on eggshells and getting to the point where it feels like we just have to say yes to everything to keep the peace. His mums more permissive in her parenting of him I guess. We've tried all sorts to help him regulate but nothing seems to be working and a lot of the time it seems like he's doing it on purpose for a reaction. Is this a normal age thing? If you've experienced similar, what have you done that's worked? X