I would assume be nicer to the director and the MD.
I know that totally sounds like a smart-ass comment, but to be honest, if there is a person that is actually observing your work, and is the producer, your boss, gives you a note about your performance, then you should take it to heart.
I think there is another side to this story, since it seems like your MD just blew up during "the discussion of the schedule". I am sure he was feeling like during the scheduling process his needs were not being met.
It sounds like there is a little bit of a control issue - just in your comment about the schedule, in that you are trying to plan ahead, and the schedule changes - to be honest, in a lot of productions and types of production, although you can sketch a week or two in advance, you are always going to have change the schedule based on the needs of the production at that time. I would never dream of setting a schedule, except for rare occasions, until the night before. (I usually at the top of day I play . . . what is tomorrow going to be if we stick on schedule and draft the call, but at the end of the day, I am usually adjusting based on how far we really got, costume fittings, vocal calls, etc.).
It does seem your Director and Musical Director are a bit stressed, and perhaps need a little more handling with kid gloves. I think one of the most important skills in stage management is to be able to "take the temperature" of the room and re-act accordingly. I love stepping into a rehearsal hall with all senses a blazing and trying to figure out who is having the bad day, who is stressed, who is panicked, and who has sort of checked out. If your producer is picking up on this, then I would try to step back and see how how your interactions with the Dir and the MD might be being perceived.
You may be nice in all your interactions to them, but they maybe perceiving it differently.