Hi, you did not make a moral mistake regarding your father's apology, but you may have made a strategic mistake.
He definitely has his issues, is a wounded person, and apparently that's all the apology he can make. And yes, he did make it worse offering this pathetic excuse of trouble at work. He is an adult. It is his responsibily not to take work problems home and inflict them on his children.
All the same, whatever partial apology he's able to make, try and accept it and focus on moving forward.
The person who talks about moving forward is correct. Even though the tendency is for violence to happen again.
Plus, parents waging war on their own teenagers and young adults, it's such a common baseline, I almost think there's something biologic about it. Not every parent does this, but many do (probably a minority of 30 to 40%).
Let me pitch an idea at you and see what you think. What if you find a boxing teacher and say you want to learn self-defense in a way which causes the minimum injury to the other person, and the person in mind is your own father. And if this instructor seems interested, maybe say you want to talk with him or her one more time before beginning training.
And that way, if you pick up on that this person is not likely to be very helpful, you can look for another teacher. And a lot of boxing is good solid blocks. But, very importantly, do not humiliate your father for that will likely only make things worse. Standard good self-defense like in a barrroom fight is a good quick jab to the rib cage, which might partially take the wind away and yelling, That's enough. Even that might humiliate your father and he might think he "lost" the fight and then think of retaliation. Even blocking blows in a showing-off way where he's your puppet, that's not so cool either. Hopefully, it won't come to this, but if it does, you want to be very matter-of-fact about it. Maybe also putting your hand on his diagonally opposite shoulder and pushing away. Medium, not showing off, even with that.
And please don't take a bunch of blows to the head during training because all that stuff about post-concussion syndrome is largely true. And an instructor needs to understand that. And just like American football helmets don't really protect, presumably neither does boxing headgear.
And also, try and be a low-key and matter-of-fact voice of sanity for your brother and any other siblings you have, and maybe also for your mother. It is a diffficult, unfair situation. Consider us here at WP as one available resource.