How would you react to an E2 who "smart mouths" you in formation?

IMMEDIATELY get in their face, lock them into parade rest, and confirm that they are receiving a direct and lawful order. Army regulations (contrary to belief) authorize a reasonable of physical “coaching “ to get him to comply. After that, the PSG, and as a last resort, the 1SG, should be involved. A counseling statement can be used, as well as recommendations for Article 15.

The NCO should be firm, professional, and SWIFT. Otherwise, every troop around will think they can get away with it. Every NCO witnessing the event should band together and put this young turd in his place.

Conjour up a page 11 right then and there

I will mass punish the entire platoon to the pint of feeling dying, but just the platoon, not him, then I make sure everyone understand that every punishment is his fault. I will cancel passes, leaves, and every single time off. I will get them every single detail...at the end, he will feel it either way.

Take sworn statements and push for UCMJ under Article 92. Meanwhile, I'd find as many meaningless, menial tasks for said private to perform until he or she recognized the fact that I am the authority figure here.

After he gets up off the floor,you tell him again! Then put a boot up his sorry ass,that is the way it was done in the army before,

In the "Old Days" it would have been - Fall Out Private and report to the PSG/Plt Ldr's Office, after we fill out your Counselling Statement for Disrespect and Failure to Obey. Of which the E-2 could possibly lose his "free time" (extra training or extra duty) for several weeks, possibly forfeit some money, and quite possibly go back to being a "Slick Sleeve" Private.

From an Army perspective I have to say the information above is not complete enough for me to really judge. My old man was in the service and was all sorts of combat arms in Regular Army and National Guard. My Mother was an Army Reserve LTC running Selective Service with a joint service command. I did Intel. The military is a huge world, and the branch/unit matters...and in this case where it matters is in understanding the soldier in front of you, and those around them. Where I was stationed we almost never saw an E2 (you had to f-up in AIT not to leave as an E3 because of the length of training). Also if you make PV2 dipshit late for work, you are screwing COL OwnsYouBNCDR's ASS by depriving them of 10 minutes of that soldiers time. Further more it was a very cerebral area. Days of PT is not an option. I say this to hopefully break what I read as a chain of very high-school bully oriented knee-jerk reactions.

What is certain is this. The Soldier needs a hard correction. The correction needs to be measured, because if you cannot measure a response then you are unfit for command, or authority. The NCO needs to know his unit well enough to be able to determine if this is a one off/single point of failure scenario in which case you discipline privately...or if it is a culture thing you make the correction to the offending private, but you do it in public where all can see the consequences.

I would also hope the NCO's next level up would take the situation as an occasion to do a pulse check with his unit to see if there are larger problems that needs addressing to include the possibility that the NCO had been conducting themself in such a way as to create the tension.

This one is simple. In front of yours troops, you explain to the dip-shit that this is not the play ground, that you expect him to behave in the same manner as the other troops. And since he does not appear to understand how things are done he can chose between some extra military instruction ( you still have that tool I hope ) which will consist of cleaning a few choice items with a tooth brush, to your satisfaction, during what would have been his normally free time that weekend, or standing tall in front of the person who can issue punishment under the UCMJ.
I say in front of the troops because he smart mouthed you in front of them, and they need to see the results, or they too may start to believe that they can slack off.

Pube patrol

Smoke his ass, if he doesn't care about that kind of stuff, NCOs have authority under UCMJ so if they're not recognizing it, a commander can slap him with extra duty or reduced pay. That kind of disobedience is toxic and has the potential to hurt readiness. find a creative punishment that wastes his free time. If you're his first line leader, unfortunately wasting his time usually means wasting yours. If you're his SL, have his TL supervise some of his corrective training to spread the workload.

Had that halo to me....his/her time off was spent doing many “interesting duties” such as sweeping the whole unit building, writing reports for other subordinates a d having them checked by said subordinates; daily duties such as this while other subordinates were off duty those souls learned not to mouth off! IE...your time can become my time with a bad attitude

In my 40 years in the military, I have never seen anything like that happen. If it had, it wouldn't have happen a second time. It sounds like someone has taken their relation ship to an unhealthy level. In the military, at all levels, you have leaders and followers. You need to know what your role is at all times. It sounds like that soldier was not indoctrened right to the military way of life. That E-5 needs to take that E-2 off to the side, away from the rest of the soldiers and counsel that soldier. It needs to be put in writing and kept at the E-5's level. Unless, the same thing happens again, then he needs to get his Squad Leader involved.

When acting in my normal MOS duties I never had a problem but it was a technical MOS which required a higher GT score. But while in Detail Branch at a training post where I ran a grass cutting team and later as what I called "The Post Commanders Head Gardner" taking care of the grounds around 3 Generals & 3 Colonels quarters using detail personnel from training companies, I would occasionally get someone who wanted to goof off. For those I had special jobs for them to do. Especially at the Post Commander's quarters where my favorite job for them would be to hand them a rag and a can of Brasso and introduce them to the brass cannon in from of the General's quarters. I expected them to work hard while there but treated them fairly & not cuss them out and would give them good breaks when they did work hard. After a couple of months of this, we noticed at the Detail Branch office where I picked them up, that they would jockey around in the formation to get in a spot where they would end up with me. Those who were frequent flyers knew that they were doled out to the teams in the same order. Had a female soldier use the excuse of being on the rag. That being the 1st time I had heard that excuse I let her do a little less. That night I asked my wife & oldest daughter and that was the last one to get by me with that excuse.

What you have here is a soldier who hasn't learned respect for the "Service", his unit and comrades, those who are in charge and no respect for himself. As the NCOIC you have the opportunity to mold a good soldier or piss off an angry one and lose a good soldier. To me it would be time for the kid gloves and in a very low voice I would kindly ask the PFC to see me after formation and go about my business of getting the platoon started for the day. You have squad leaders to see that the work gets done so you can spend some time with the errant PFC.
I'd then take him to the mess hall, get some coffee and wangle a snack out of the cook and have a seat where there are no people nearby. This kid has a problem and thinks nobody cares. You need to find out what the problem is and see if you can help. Could be some little thing in his platoon or something big back home that the kid has no control over. Help if you can but by no means do you berate the kid nor give him hell and any punishment at this point. You already have his attention by being nice to him so make use of that and send him back to his squad or unit with the reminder that he is a soldier first last and always and he needs to conduct himself in a respectful manner at all times. I'd keep tabs on the kid through his squad leader and my own observations with brief chats on occasion and encourage the soldier to keep at it and do the right thing. The PFC pushed you to the wall and you gave him a break. He didn't expect that and now owe's you something in return and he knows it. If you get the favor repaid that's great. If not there are many ways of handling a recalcitrant trooper. I'd try the nice way first and the worst way last if he didn't improve after that. Hell, it worked on me so why not him? Been there done that.

Tell them to bring a battle buddy and see me after the formation. They and their buddy will do the task and the pvt will get a counseling reflecting his or her behavior.

End it right there. Keep the formation as is and Pvt Ass Wipe gets an ass chewing and an explanation of the importance of carrying out all lawful orders given by those above him. Pvt. Ass Wipe gets an Article 15 with a recommendation that his military service be terminated after a few months in the stockade.

PT his ass until he drops! Then give him an Article 15, reduction to E1, extra duty, and restriction to post for 30 days! You have to show him and everyone else that this behavior is NOT acceptable and that there are consequences!

PT his ass until he drops then give him an Article 15, reduction in rank to E-1, restriction to post for 30 days, and extra duty! Make an example of him so everyone else will know that this isn't a game!

LTJG (Join to see) Well, I realize the photo doesn't necessarily correspond, but I can't help including it in my response:
Step 1: take those PT belts off
Step 2: have troops dig a big hole
Step 3: throw PT belts into hole
Step 4: fill hole
Step 5: smoke the E-2 like a cheap cigar

As an Ex NCO (AJ E-4 - for clarity) - I would pull the wise ass Pvt and his / her team squad lead to an office / separate place and set him / her straight - orders are orders and thats it... nip it in the bud....complaints come later...compliance is paramount right now.... As a Commissioned Officer ( which I was later in life) - I would simply monitor what the NCO did and intervene only if need be and then (maybe) whisper into the Pvts ear after the NCO was done that he had better take the advise of the NCO and move out....