Does being an instructor exempt you from parts of 670-1?

Nope, I instructed at the schoolhouse at Fort Eustis, we were still Soldiers  whether on the podium, on the floor, or at the gym, AR 670-1 applies to all Soldiers, regardless of rank or position unless otherwise directed by the Commander. And it had better be in writing. There is no good reason to have your hands in your pockets while teaching. No operational requirement such as a beard for SF Operators, and it isn't a safety hazard such as tsking off your ID tags while on top of a helicopter. Have her show you where in AR 670-1 or a local SOP or Command directive where it states that. If she can't do either of those, then she is just plain wrong and should be an NCO enough to admit it. I have slipped and done it, and I have caught myself a few times and my Soldiers have caught me a time or two, to which I said roger that and pulled my hands out of my pockets and made a conscious effort to not forget.