Keep calm. This is exactly where you should be.
Apocalypse World is about telling stories from out of the wastes. They're not all happy stories. Maybe this is the story of how an army bearing down on an oasis of safety made people tear themselves apart with worry before it even got over the horizon. But as long as everyone's cool with seeing where that story goes, you're not doing anything wrong in telling it.
(Before we start, you don't mention the second edition, so if you don't have it you should definitely grab it. It might not be 100% compatible with your game setup but the ancillary battle & chase moves are nice to have and it's got quite a few more sections of advice on how to run moves as PC vs. PC.)
0) Wait, is everyone cool with seeing where this story goes?
So, Keeler wants to go off and kill Dremmer, but Uncle thinks he can bargain with Dremmer and tells his guards to restrain Keeler. She's having none of this and shoots her way free.
This is great if: Keeler and Uncle's players are both being honest about what their characters would do. Keeler really wants to burn her history with Uncle for a shot at Dremmer, Uncle believes in diplomacy enough to come to blows with Keeler. They'll react to setbacks and interference in keeping with their characters, and are willing to succeed or fail depending on how the dice land.
This is terrible if: Keeler's player wants to play a shooty game, Uncle's player wants to play a talky game, and they've turned to the rules of the game to decide which one of them should be right. Keeler and Uncle are just pawns in that struggle. They'll take setbacks and interference as attacks on their philosophy, to be annihilated, and won't accept it if the dice don't land their way.
It's never all one thing or all another; people are large, they contain multitudes. Just in general, you should be using some kind of safety tool at the table, but especially keep one in mind when PCs are endangering each other. If they're pointed at some pawn of the MC, well, you've got those in infinite supply as long as the world endures. PCs aren't that fortunate.
1) Ask provocative questions and build on the answers.
Especially now, when you're not just asking for you - Keeler and Uncle need to hear about each other, too. If they've got history, remind them of it; if you're worried about the PCs splitting up and having a running gun battle around the hardhold, you can just come out and ask it: "so this is really what it's coming to, then? Pick sides, fill your hands, last one standing wins?"
Keeler and Uncle's players might be a little antsy about talking about their plans openly - if Keeler talks about climbing up the sniper tower in the dead of night, Uncle might want to tell his guards to tear it down, just like that. But you're there to make the world seem real. Uncle's got no idea what Keeler's doing, so tell him the consequences and ask - sure, he can browbeat them into doing it, but they'll think of him as a paranoid maniac and rightly so.
You can also use questions to frame this disagreement in terms of the history (Hx) characters have, but never played. "Uncle, how do you deal with violent people fairly?" "Keeler, have you snapped like this in the past?" Life in the wastes is a violent thing; it's unlikely that people can't forgive. If Keeler and Uncle want a way back, you can work out how to give them one.
2) When chaos breaks out, it's important for everyone to have a go.
First of all, emphasize that we have rules for this and we're going to follow them. When it turns to PC vs PC, everybody wants to start shouting all at once and race to be the first to roll their dice, and that's no good.
Then go around the table to find out what everybody's going to do, but have them hold onto their dice. Don't let them roll yet. Everybody gets a turn to say what they're doing, and they can change their mind if they need to, and nothing happens until everyone's had their say. Include your NPCs.
-- Apocalypse World 2e, "Moves Snowball", p.132
This doesn't have to be "what move do you make"; it's just "what do you do". Some people might just be doing something unopposed, or want to see how things are going to break before they do anything, and that's fine. Once you've finished resolving pass 1, you can come back again if everyone's still pulling in their own directions.
Some things to keep in mind when you're resolving:
- most of the time, "opposed rolls" can be played as one player rolling a move, and another player rolling Hx to interfere
- if you're seizing by force to exchange harm, consider putting the exchange of harm on the table and having both people roll and make choices secretly, revealing at the end - both people taking definite control of something means it's still contested or perhaps that they've each got clear control of half
- rarely but dramatically, both players can roll a move, and then both roll to interfere with each other; usually this plays out over more information-gathering moves where both people want to know something and neither wants the other to find out
- keep in mind aid/interfere is limited to one party per roll and might be better off going to people on the periphery who still have a stake
Treating all sides fairly and pulling out information about motivations are not, in themselves, guarantees that everybody will be cool with the way the story's going. That's what safety tools are for. But by making use of them, it'll be easier for you to plot a course forward that's a satisfying story, true to the characters, and keeps the players happy.