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

Set him up for failure!
Recommend Soldier for urinalysis, then counsel on duty performance as "Consistently late"
Refusal to submit to drug screening is grounds for "Suspicion of deception" because refusal to show dilated pupils is an indicator of substance abuse...do so publicly, but not maliciously:
"Sunglasses again? Ok, random drug test after formation...oh you can keep them, paperwork is already started." -Classic passive aggressive

I would council him/her in writing about the wearing of unauthorize sunglasses and put them on a few days of extra training.

I would suggest you take them off, put them in your pocket and tell the soldier he will get them back at the end of the day.

If the formation is moving. Call an immediate halt. Announce to the formation that you are going to keep them there, until you decide whether to seek non-judicial punishment against the troop for violating regulations, and disobeying a lawful order. Then place them at ease, and let peer pressure take it's course. If after a couple of minutes the disobedient troop hasn't complied with your order, pull him out of formation, and have a ranking individual take over the formation, so you can escort the troop to the First Sergeant and have him/her read their article 32 rights... If peer pressure works, have a counseling session later that includes the troop's supervisor and First Sergeant. Sometimes letting the troop see the Manual for Courts Martial and the punishments authorized for the crime, brings them back to the military reality.

Disobedience of a lawful order. Due process and chain of command. Without obedience, there can be no order or discipline.

First thing you have to do as a Non-Commissioned Officer is look in the mirror and ask yourself how did this come to be. E-4's and below are never wrong, they are only as wrong as we allow them to be. Bring the soldier in sit him or her down and see if their is any underlying issues. UCMJ should be the last recourse for a Non-Commissioned Officer (unless it is a serious offense) you have plenty of tools in your toolbox to correct this trivial issue. There was a time when the NCO Creed stood for something.

After I had disposed of the offending eyewear I would come up with a training exercise to be undertaken by errant young Soldier/Sailor/Airman/Marine that would set forever in their brain housing group the importance of, "cheerful willing obedience to orders". And how failing to adopt a correct attitude could possibly have a detrimental affect on their future military career, not to mention their immediate health.

You have to due to the fact that the soldier is disrespecting the NCO in front of the other soldiers. This was probably not the first time. As a NCO you must demonstrate to everyone that this behavior will not be tolerated. I think I once read something about disoberying a lawful order. I'm sure there is some sort of UCMJ punishment for this.

Have a meeting with First Sergeant, yourself and the Soldier. It will take the pressure off of you. The 1st Sgt. Should document the meeting for future problems. Find out what's behind the resistance.

Unless they are prescriptive sunglasses and medically required, this person is disobeying a lawful order. He or she is subject to the UCMJ, article 15, NJP. As being an old Gunny I would probably just remove them and crush them into little pieces and if the whiner goes complain to some softhearted superior so be it. I have no issues in having a back room talk with any of my superiors, especially when it comes to a Marine, Soldier, Navy or Air Force person disobeying a lawful order (Article 91—Insubordinate conduct toward warrant officer, NCO, or PO).
Elements that pertain to disobeying a lawful order
Disobeying a warrant, non-commissioned, or petty officer.
(a) That the accused was a warrant officer or enlisted member;
(b) That the accused received a certain lawful order from a certain warrant, non-commissioned, or petty officer;
(c) That the accused then knew that the person giving the order was a warrant, non-commissioned, or petty officer;
(d) That the accused had a duty to obey the order; and
(e) That the accused willfully disobeyed the order.