There are a lot of stage managers who would like to think they are the "Authority" or Power, but reality, using words like "responsible" or "leader" are perhaps better, but at the end of the day we are just middle management, easy to have some one step in above us.
I feel like any stage manager who demand "authority" (ala Respect My Authoritah!), is reaching for a last straw - and sometimes we all get there - but if we are demanding it, we will find how little we have.
We don't have the power to hire or fire, but we do have the ears of lots of people who do. We do document the show for the producers, so we are indeed starting a paper trail for those people who make decisions "I see here, by the SM's reports you were late four times to show calls . . . ".
Directors in the professional world are a very trick bunch, and if a director wants to come back note, tweak, change a show after opening, I really bump it up to the producer. In the heat of the moment, I would defer to a director - but that's because it's usually a director who will get me hired. (Now, safety trumps all of this . . . I will not do anything unsafe). Now, if a producer wants me to do something . . . well, again, as long as it's safe, they are paying me, they are the boss. NOW, I will, in all of these cases explain the situation and what their choice and request may require . . . "Oh, you want us to drop 500% more glitter on stage, you do that will require another hour of clean up, and put us in overtime, meal penalty and, even then, we might not be set for the evening show . . ."
It's very heard to remain a leader for a show, when you have a level of management above you that steps in (and often times seems to under mind your authority) - just remember, that you probably never had it to begin with.
That's why parenthood is good training for stage management - responsible for, never in complete control of . . ."
As far as someone else calling cues, there are, on some contracts an AEA rule stating that only a SM will call cues except in the case an emergency.