Originally Posted by permanentvacation:
She was constantly telling the substitute things like, " You can't go in that room." "You're not allowed to do that" "You're supposed to do this" "I don't think Ms. So and So would like you going into her refrigerator" No matter what my sub did, the 3 year old child reprimanded her for it and told her she wasn't allowed to do that or was 'supposed' to do something else. The sub constantly, nicely - in my opinion too nicely which is why the child continued reprimanding the adult 
told the girl that what she was doing was just fine, or explained herself to the child saying things like "It's okay that I'm going in Ms. So and So's refrigerator. I need to make lunch for you."
So, yes, the child was literally reprimanding the adult all day and telling her what to and not to do!
This sounds like a child that needs to be told who is in authority. I would be the one addressing this and letting the child know this is totally unacceptable.
The assistant is "my" helper and you, as a daycare child are NOT in charge!
If the child continued with this behaviour after it was discussed with them, then yes I would talk to their parent.
I've never had an issue with a child once they understand and realize the limits that need to be imposed.