It is extremely common for one or two of the assistant coaches to be in the corner for a particular wrestler and for the head coach to be off to the side. The best person to be in the corner is the person who trains and drills directly with that individual on a daily basis - and it will be a different combination of coaches for each wrestler. And sometimes, it becomes obvious after all the training they do that one assistant coach is just perfectly in sync with a particular wrestler and knows exactly what to say or not say at a particular time. You go with that combo.
Absolutely common.

Think of the football analogy. If a head coach has developed a great core of assistant coaches, the offensive coordinator is the main man when the offense is on the field, and the defensive coordinator is the main man calling shots for the defense. The head coach is there to watch, consult and give input, but he is deferring to the coaches who work with those players most closely.