I can appreciate that you are feeling very hurt...and with good reason. After all you are entirely blameless in this scenario.
I don't think you should do anything at all for a day or two, then, when you are feeling a bit calmer, try to work out what you want and if it is going to be possible for you to get it.
I would guess that ideally you want your Dad to humbly apologise for the mix-up, the row with your Mum and most of all for speaking to you in such a terribly unkind way.
I would also guess that this is very unlikely to happen.
So...you have to figure out what else would make you feel better about both yourself and your Dad. Maybe when both you and he are calm, telling him how hurt you were by his words and actions would help ?
If you do this, though, you *really* have to try to stay calm and stick to just saying what you want to say, not entering in to any kind of discussion with him about anything else.
Alternatively, you may feel that he has just crossed a line and any further approach has got to come from him. Your call.
One last thought...does he have an alcohol problem ? It is absolutely no excuse for his behaviour, which was truly shocking, but , if he does, it would be something to take into account when you next have any 'important' conversations with him.
Good luck.