What do you do when a soldier refuses to listen to your directions?

I see three issues. First, a lack of respect for you as a non-commissioned officer, which you must fix quickly. If the Soldier is unwilling to obey your lawful orders, but will obey others, then you need to do what is necessary to fix his lack of respect for your authority. If he has no issues obeying the orders of others, than this is more than likely a personal thing with you than authority in general. This is a tough question you need to ask yourself, why would he have little respect for your authority as a non-commissioned officer? Is there something there you need to fix as a leader or is this just a punk-ass kid who needs to be taught a lesson? Serious introspective question, which you should not provide answer in this public forum. Always ask this question first, and you will become a better leader over time. None of that last internal question negates what he did, which must be rectified.
Second, as a company commander, I told my NCO's and Officers I would back any recommendation for an article 15 provided the case met the following criteria. A) I could clearly read the entire story in the counseling packet of why this Soldier deserves the elevated punishment. The Soldier's chain of command should NOT have to verbally justify their reasoning. I should be able to pick up the counseling packet and read everything. There must be frequent and consistent misbehavior where the NCOs have made the developmental steps to correct the problem. This is the standard the JAG has for the commander when they hand the JAG the counseling packet. Great NCO's understand this, and become far more effective at discipline. They recognize the JAG may advise a commander against an article 15 based on a lack of justification. This reflects badly on the commander to his superiors, but it also makes the NCOs who recommended the article 15 look toothless. B) The act was so egregious the act alone is worthy of an article 15, AND there is a counseling stating the facts and recommends an article 15.
Third, why did none of the other NCOs pounce on this Soldier for disobeying you in such a public manner as a formation? His disrespects reflects negatively on them as well. One of the finest units I was ever apart of had a junior NCO corps that took their role seriously, and backed each other up rapidly. If a Soldier was witnessed being disrespectful to an NCO, every NCO within a mile was there to tear into this Soldier and bring them on line. This was done from corporal through SGT. The life of a Staff Sergeant was much easier based on the fact the E5s ran their sections with an iron fist. Phenomenal unit and very few company or field grade article 15's. Everything was handled at the lowest level and Soldiers were afraid to disrespect anyone.

All this UMCJ talk. What happened to making his life hell for a while with a lot of extra activities. Make him/her think before saying No. Try and re-education them the proper military way and if that doesn't work, them submitt the paperwork

When I was a squad leader, a LCPL refused a direct order. There were 2 guys straight out of Infantry Training School standing next to my room waiting for me to assign them a room. These boots were going to be assigned to my squad. We were in the process of cleaning the barracks when I told the LCPL to go help clean the head. I don't know what crawled up his butt, but he refused stating that he lived in town and shouldn't have to clean up. I told him that he walks down our hallway and uses the head, so get in their and start helping. He refused again. Mind you, the new guys were watching what was going on. So I told the LCPL to get in my room where I gave him a good wall to wall counseling session. I then opened my door and drug his half conscious ass back out in the hallway and dropped him in front of the new guys. The new guys turned out to be outstanding Marines. The LCPL called his mommy and she called her congressman. A week or so later I was standing tall in the 1st Sgt.'s office along with the company Gunny. I told them what happened and they told me they would not press charges if I went down to the barracks and beat up a different shitbird, which I was glad to do. In that particular case, I felt I made the right decision. Gotta love the old Corps.

The specialist needs to be made an example of or this kind of behavior will continue with the other soldiers in the unit. I would first have the E-5 counsel the soldier with the Squad Leader present. Then, on the 4856 refer for an Article 15. During the Article 15, the TL, SL, and PSG is present during the proceedings (of course the soldier is innocent until proven guilty) and the chain of command would request the commander to suspend the sentence. If he misbehaves again, vacate the suspension and Article 15 again, (of course the soldier is innocent until proven guilty) drop the hammer down on him to show the rest of the soldiers in the unit that insubordination will not be tolerated. The word will get out in the "Joe Mafia" that this behavior will not be tolerated and the Chain of Command supports the leadership down to the TL level. If it continues, Bar to Re-enlist and chapter out for Misconduct or Failure to conform,

It's a general question but there's no general, or cookie cutter answer. Every Soldier you lead is different, each responds in their own way. While the grab and smash style may work with Smith, with Jones you may have to put him your arm around him, steer him off to the corner and talk sense to him. And there's everything in between those two extremes. A leader must have the ability to read their subordinates and apply the right motivation for that person. When I was a young sergeant my first sergeant at the time told me "anyone can lead happy Soldiers, but it takes someone special to motivate someone to do something they don't want to do". And he was absolutely right...

Take the damn glasses and have him report to you after formation and have his/her ncoic present and award manual punishment. There is no need to ruin an enlistment for a small fraction but if he refuses your punishment then hang him/her out to dry.

If this soldier doesn't have a profile for mentioned sun glasses. Talk to him about this matter in private and with no witnesses present, kick his ass, smash the glasses and warn him/her he/she will have glasses shoved up their ass if this occur in the future. PS: Leave no marks on said soldier, use rolled up news paper, rubber hose, etc.

I am currently in the process of finishing my packet for ocs to join the ARMY as an officer and it's small things like this that make me worry I'm going to get kicked out for beating someone down. As a Sergeant in the Marine Corps I wouldn't have had to face this. Even our shit bags had more respect than this and their peers would have beat them down in the formation if they saw someone doing it before a senior ever had to see it. Personally I'd make the whole formation suffer for not policing their own, as an enlisted of course. God only knows what I'm going to be able to do as an officer.

If you have established your authority as an nco through competence and commitment to your Soldiers, this will rarely, if ever hapen. It also doesnt hurt for them to know you could choke them out faster than they can say "Please stop sergeant! "

SMOKE SESSION
IN MY DAY YOU WENT INTO A CONNEX AND FIXED THE SOLDIER