Ah ok hehe.
Then that would be perfect I think the struggle of the people wanting to leave the vault and those wanting to stay.
I think this would be good because, at this point the overseer is starting to loss power over the vault as population splinters and this new group wants to leave. I think maybe he makes it into more of a democracy to show this splinter group that they are wrong since so many people want to stay (but they are people either under the influence of the overseer or are scared to leave. So this splinter group has to try and convince the others to leave, since they can't make it on their own and they need to follow the "democracy" that has been setup.
So the roleplay would all revolve around the splinter group trying to convince the others to leave and the others trying to convince them to stay. The struggle behind this disenfranchised splinter group and maybe some of them go on strike which would cause huge issues inside a closed society like that. Also, the other side of the coin, the fear of braving the wasteland and trying to start a new leaving the safety of the vault.
Yeah, you got me confused. 
The problem is - that "normal" RP doesn't let the people stay there. If you only stay around the whole day and chat nothing will happen and players lose interest. There need to be little "events" even when they are small, like a computer got destroyed and the inhabitants must repair etc. Or give the players a little daily job, just a tiny one asided from the chatting. Otherwise it will be the same like what happened in the hub - no progress - the players lose interest.
I agree, I think the point is that, using my scenario for example, you need to have a GM who is maybe the overseer, and a GM who is maybe the leader of the splinter group and they have to kind of give out the tasks and events that occur, directing the story that evolves. This sounds like it is suppose to be RP not just a safe place to chat. If it is RP then I would assume there would be events and an ongoing story that is changed and played out through the players actions.