Sorry but a lot of it does sound normal for the age: you need to plan for it and decide:
when you are going to have to keep her under restraint (e.g. reins when out walking to keep her safe)
when you bring her back to watch the film and when you let it ride (the halfway house of not making her conform to your will but getting angry is the worst option)
when you are going to make her share and when you are not
when you need to keep her under surveillance (e.g. in somebody else's house)
when you are just going to ride out a tantrum
When my dd was her age, I did not even go to the bathroom alone because I thought she might seriously injure her baby brother. She has grown up into a lovely, caring adult with beautiful manners and on very good terms with her brother. Just stay calm, firm, but don't show her that she's flustered.
At this age, all the good behaviour doesn't have to come from her: if she doesn't run away because you've got her on reins, that's fine; if she doesn't hit her brother during a tantrum because you are holding her hands, that's fine; if she follows you when you go out because you are physically holding onto her arm, that's fine
Eventually, she will internalise that there isn't much point in trying to defy you because mummy gets her way anyway.