Your brother's behaviour was completely unacceptable, but it seems odd that you would choose to discuss what appears to be an ongoing contentious issue while driving,
If you found it necessary to pull over and park up, why didn't you say that we're not going anywhere until we agree that there will be no further mention of the subject instead of (presumably) continuing the debate?
In saying that you 'don't know when to shut up', could your mum have a point? Have you martyred yourself by taking on your brother's problems and berating your brother over his apparent inability to get a job, and has any discord between the two of you taken its toll on your mum?
If your mum needs support or coping strategies to deal with having her 31-year old unemployed son still living at home, I'm sure you can find a way to help her without finding it necessary to confront your brother or otherwise comment on his shortcomings unless she specifically asks you to do so.
With regard to your brother's violent outburst, is the first time he has vented his frustration in this manner?
If so, I think you should endeavour to forgive him while making it crystal clear that should he assault you again you will report him to the police.
Please note that forgiving is not the same as forgetting, and until you have confidence that there will be no repeat of this type of incident you're best advised to keep your distance from your brother.