It's not OK to hit our at someone because they are shouting and swearing at you.
I cannot tell you how many times someone has done that to me but I never felt the need to shove, hit or otherwise touch them.
I may have sworn back, told them to shut up etc but not assaulted them.
The test is would a police officer arrest you and charge you with an offence solely based on you shouting (non discriminatory of course).
No, they'd warn you and get you moving.
Would they arrest and charge you for shoving someone hard? I expect so!
Because it's a sibling has no barring. Those that say there is no power imbalance because they are siblings - hello, he's a male and he's older - of course there is.
Id have much more sympathy for this girls brother if he sincerely apologised and agreed he may need to seek help for his temper. If he did this I feel a stern talking to would be enough at this stage.
But he's not acknowledging what he has done and he's not apologising. He's disrespecting his parents as well now as he's shutting down communication. This is what would make it tip it for me for wanting him to move out as he clearly doesn't care.
Evening If I felt I wasn't in the wrong, if I had made someone feel so frightened of me and sad you bet I'd apologise!
Id investigate into whether he is taking drugs if his behaviour is normally completely unlike this. But if he won't seek help and admit to what he's done you need to put the more vulnerable person first, which is your daughter, OP. .