So a little backstory is that my mother died nearly 4 years ago and my father is taking care of my brother and I. However lately my brother has been talking to our dad in a very, very poor manner. All of us occasionally fight but it lasts only a short while and doesn’t happen often. My brother though has been lashing out at our dad for literally no reason. Even when he asks my brother “what are you doing?” my brother yells at him for a good two minutes and even when I try to settle him down it just doesn’t stop. It was going good three weeks ago when my brother decided to work with our father and I (we own a small business) but my brother quit out of nowhere two weeks ago. After that he just keeps yelling and screaming at our dad for no reason. We think maybe my brother’s new girlfriend has something to do with it (we noticed he changed for the worse ever since she came into his life) but we don’t want to blame anyone. My brother may also be bipolar but he was never diagnosed.

What can I do to help both my father and brother?

Do you think your brother would listen to a civil conversation? It's possible that if you sit him down and talk about it, he might calm down.
How old is he, by the way?

>>2 He is about to be 24. And sometimes I talk to him politely about it but it usually ends up with him just saying that our father says stupid shit. He’s very stubborn.

Im sorry for what you've been through. This backstory about your mother, maybe it has something to do with it? Did your brother ever behave like this before ? In the past ? With your father or someone else ? How long he's been doing like this w/ your father ?

The problem seems not to be between you and him, but clearly between him and his father. Unless both have a civilized conversation and open their heads and set limits and boundaries and a communication of their impending problems, it could solve his behavior. And your dad needs to impose his figure as the leader more, as it isn't acceptable of a person to talk poorly to their parents, unless their parents are truly horrible. What doesn't seem to be the case at least.
Don't try to be the middle of this, because it will only tire you and don't solve anything. You can only try to reason with them that they need to talk, if they don't, its not your responsibility. If you keep worrying about it too much, the stress will just accumulate. Take care and stay healthy!

Maybe ask your brother about some examples... what is it exactly your dad says that makes him so angry?

Example: Your brother may be depressed. For depressed people, "how do you do" can seem like a provocation.

Don't blame your brother lightly. In my family, I had the situation that my dad treated my sister like a loving father, while he was an asshole towards me and my mother.

Things can be more complicated than they may seem at first glance. My best hint is... tell your brother how you feel about it, but avoid blaming him at all costs. Maybe say something like "I just want to understand it".