If your SM is not cutting it, you are not there to punish them for it.
Unfortunately, the people in charge sound like they refuse to reconize their problem. Iit's hard to fathom why such a person would get a SM's position if they give no outward signs of taking it professionally. Maybe the same attitude that won't fix the problem helped create it in the first place, lack of awareness of the skills demanded of people in that postion or of which people possess them.
That said, maybe this person is very competant when it comes to running a show, just not an anal list-making type.
But your job isn't only to assist a SM when they are doing everything perfectly (by whatever your definition might be).
You have two good choices,
One, decide everything is so messed up that it's better not to be involved, in which case find a polite way not to be involved while there is still time to repalce you. The damage from particiapting would have to be a lot worse than the damage from your pulling out. This would have to be a pretty extreme case.
Two, step up and do what you think needs to be done to make the show run properly. Organize everything in sight, keep the prompt script
, attend all the meetings with or without the SM, learn the script by heart, work on the technical and personnel questions and take that as far as you can.
Draw the SM into whatever issue you are addressing: "I was thinking of XYZ and wrote this up (plan, schedule, assignements) . Do you think it makes sense? Should I change it?"
In short, the SM's poor behavior is the opportunity for you to demonstrate your talents.
Don't try to upstage her or suggest to her or to others that she is no good. Communicate your leadership abilities by your good example and the truth will become clear
to everyone before too long.
And even if she is personally unpleasant, so what? You don't have to be best friends or friends at all. You'll certainly work with people you don't like again, whatever you do in the future. Don't let them bother you. Don't work with them again, but don't let them bother you in the meantime.