Aikido martial law protocol actually takes a back seat in this situation to the individual's cultural and will.
I've been in Aikido a long time, but I've certainly never heard of anything like an "Aikido martial law protocol". People get challenged for the leadership of groups all the time - I've seen it in dojos in the US, and I've seen it in dojos in Japan, there's not much difference.
It's not that difficult - the current leadership finds it a problem then they need to stand up and deal with it, just like they would in any other part of their life.
Same for the members, if they're bothered by it then they need to stand up and do something about it it, just like they would in any other part of their life.
It's nice to think that everyone will play nice together, but it just doesn't happen, learning to deal with that is part of the process.