Should I run away?

I haven't dared think of doing so for a while, but today my dad and sister had a fight over a misconception and I don't know what to do.

We were in a restaurant and she was constantly poking jabs at him (e.g. telling him to give her the phone because it was one of those places where you have to order online and he was taking a bit long, saying he should treat the waiters nicer because he's generally a serious person when speaking to people for business' sake, etc.) and he got irritated and said that she was criticizing every little thing he did.

While she was, they have a very strained relationship and this isn't really the first time she's done this, though it is the first time I can recall him getting openly angry about it. They fought a lot when we were younger, and she's definitely lost a lot of respect for him because of that.

Both of them have anger issues, and use to head butts a lot (still do, but less so) and I'm honestly scared. I'm not good at talking about things and I worry it's taking its toll on everything, especially my mother as she always has to diffuse the fights and transfer information from one to the other.

Also, my dad tried to talk it out with my sister and she kept telling him to go away, even to the point of yelling. He got ticked and went to my mom and said my sister told him that we were taking her side (she did, just to clarify). They're out for a walk now and as soon as they left, my sister looked at me from down the hallway, spoke to me, and when I asked her what she said, asked if I'm ignoring her. I can't remember if I legitimately didn't hear her or if I just didn't want to answer because I knew she'd be really tense and stuff, but I digress. She asked what I was listening to (I'll assume that meant she thought I had the music too loud to hear her) and I said I was watching a video. She came over, plopped on the couch, and although I can't remember exactly what we said, the conversation basically went where she asked what I was thinking (I was silent for a bit), and I said nothing much. She asked again and I asked her if there was something she wanted me to be thinking about. She said she wanted to know if I was thinking about her argument with my dad when he came to talk to her, and I can't remember what I said, but at the end of the day, I said both of them were wrong. She said I hated her, walked off, and said she hated our dad. (Keep in mind that this is a bit of simplification; I can't remember exactly what she said but I think this was a mental self-defense mechanism or something.)

I just watched this short and it's making me wonder if I should leave this place. I know I'm probably overreacting, but this has been going on for so long and I just want peace. I don't know if I can get that here. My mom doesn't want to send my sister to therapy and I doubt she'll want to send my dad, herself, or me either. If there's anything specific you want to ask, feel free to, but please respond with genuine advice. I'm tired and I just want an answer.

I don't know if I can take the thought of them all being in panic if I leave, or if I'll be able to handle myself on the streets, but I don't know what to do if I stay.