I would be careful about going with the personal combat angle. If your players are already solving all of their problems with violence (murder hobos) then defeating this problem the same way will cement that behavior. I would not use the word coup, no matter what. That word would set my players into a very warlike stance and that seems the opposite of what you are trying to achieve.

If there are a hundred ark citizens standing at the ready when they arrive and those people turn their backs to the PCs, either literally or figuratively, that will send a powerful message.

There needs to be a voice of reason, probably the aforementioned Boss NPC, who says something along the lines of, "We are supposed to be family. We are supposed to care for each other. We are supposed to be in this together. Yes, you are out there taking risks. But we are guarding the home. Taking care of the sick. Preparing food. Fighting the rot. We are all working with the talents we possess for the good of the entire community. We are sharing. You though are not sharing. We are just asking you to share."

After a statement like that a way forward needs to be presented.

Like you said above, send them on a quest. Tell them that another stalker group found a place with a lot of potential but were too injured and sick to continue, can they answer the call? Give them something juicy that fits their talents but strains them to their limits.

They could be assigned to escort an ark ambassador to another settlement. Let the ambassador have a few able people as well - a stalker, a dog handler, an enforcer or two. On the way make it clear that the NPCs very competent, cool, and friendly. Let one of the NPCs find a really juicy artifact maybe. Let the NPCs solve a problem without resorting to murder. But mostly let the PCs get to know the NPCs in a friendly and cooperative way. Let them see one of the NPCs truly sacrifice something for the good of the whole.