The house is so peaceful when I ban the tv, but the minute it comes back on the kids are screaming and fighting and hitting again. Should I just get rid of the tv?
One of the things to keep in mind is that most of us don't come into unschooling with very good skills or etiquette around video media because we don't have the experience. We, the adults, have a learning curve - and that's part of why we end up blaming crankiness on tv and video games, because we don't even realize there are skills to learn.
Take the idea of "tv" out of the picture and substitute some other activity or story or toy and what do you see? What are the Specific issues? And how would you solve those if the kids were doing something you considered valuable or beneficial?
If the kids are fighting, are they disagreeing about what to watch? What would you do if they each wanted to work on a different project on the same table and there wasn't enough space? You wouldn't just take away all their materials, right? You'd look for ways to give them more space - move one to a different table, or onto the floor, or help them organize the space better so they weren't running into each other. Maybe you'd stand and hold things for them, or carry items back and forth to shelves so they could keep working in the limited area. You'd problem solve and figure it out.
You can do that with video media too - set kids up to watch or play in different rooms, or in the same room but using headphones, or in the same room but with the screens (and speakers) angled so they don't interfere with each other. I have a very small house, and we've rearranged the furniture a few times so that people could ignore each other - or so a kid could play a video game, or build, or draw while also watching a movie on another screen.
If they're quarrelling for other reasons, what are those reasons? Does someone need more attention? Do they need an adult on hand to help them communicate and work things out? Maybe you fell into the kind of behavior patterns you learned from your own parents and left the room the moment the tv was on - used the tv as a babysitter. TVs aren't very good childcare providers ;) You know that, so don't set everyone up to fail. Treat it like a set of art supplies - you wouldn't leave a pair of toddlers alone with scissors and glue, right? You'd be there to help.
Maybe the tv isn't in a great location - sometimes when adults are anti-tv they try to make it unappealing by putting it someplace awkward, or setting kids up so they have to choose between watching tv and doing other things. Those sorts of things can create stress that gets expressed in conflict, so it's a good idea to make video media more convenient to the rest of life. Make it easy for kids to eat, play, dance, build, and create with a video playing in the background. Don't set them up to have to be frustrated or to have unmet needs in order to feed their minds.
I definitely want to affirm that sometimes videos for kids can push a lot of buttons for us adults. Some of that comes from thinking about content in terms of lessons rather than experiences - we worry about what various shows are "teaching". But as unschoolers we know that teaching isn't learning - so it can help to touch base with that understanding. Kids aren't simple sponges, soaking up knowledge, they're people interacting with the world. They're active participants in their own lives, their own learning - and a huge part of that is about how they interact with the people close to them. What We do is much more important than anything they see or hear. If we turn our backs on them in disgust when they're doing something they enjoy, they learn some pretty ugly things about human relationships
Something that can really help is to step back from the idea of "your child" when they're watching something they like and instead think about how you'd watch the same thing with a good friend who wanted to share their joy with you. You might not enjoy the same thing, but you also wouldn't be looking at the program like it's a kind of lesson you need to monitor and correct. That shift in focus can actually change how you see the show! And it can be a kind of "aha!" moment in terms of how you see your interactions with your kids. Shifting your own mindset can change a Lot of things.
It can even change the way we respond to the voices and music we hear on kids' shows. A lot of those voices are pitched high and... "perky" in one way or another, and that can be grating to a lot of adults. It can be helpful to recognize that the reasons those voices are grating isn't just about our different adult auditory apparatus (which is actually less sensitive than a child's), but about the baggage we've picked up along the way, the things we relate to those tones. They're a lot like the tones adults use to coerce kids, or salespeople use to manipulate customers... but they're also the tones friends use when they're sincerely excited about things and want to share them with us. It's not really the tone making us flinch, but the old feeling of "I don't want to and you can't make me." Knowing that, it's possible to step past that visceral flinching and see what's fun and interesting from our kids' point of view.