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

As an NCO I would have quickly corrected it. Now I let other NCOs handle it.

I'm with PO Thomasson.
I probably would have told him he didn't have to do it, give it to someone else, then make life one long latrine cleaning adventure until the light dawned. The first time. Automatic write up for anything after that following proper proceedure

PRETTY DAM EASY ! As an E5 to an e2/3, wack him up side the head or UCMJ the smart mouth for disrespect & in subordination. If you give the person that just means some one else has to 'supervise' him.

Give him the day off give all his buddies double duty

tell them to lock it up their at the position of attention. then take him or her of the side with another NCO and have them explain themselves. Sometimes an Art 15 or personal counseling will fit. Explain to them there is a right way and a wrong way to say things in the Army but commands can never be left open for the individual to follow.

From my humble view, and I got out in 1993, I had the same thing happen while deployed; A PVT said "no I will not do it". I asked him again and explained that although it is no ones favourite detail, that this is mission essential and I only choose those who I know will get the job done". He stood his ground and balled his fists and clenched his teeth. I made the statement that he needs to go cool down and we speak later.
Later in a one on one he simply said he is tired of being in the desert and he is sick of being the private, he could not see the importance of this task for the mission. I let him go with a warning, counselled him and said that setting the example goes both ways; up and down, that he is a good soldier and I too am ready to go home so lets let it go.
the CSM heard all this and told me I did the right thing but at the next smallest detail, I need to lean on him hard.
That night I made the rounds to check the guards on the perimeter, I looked at who was missing and it was the same PVT, fast asleep in his fart sack...needless to say he got an Article 15 the very next day. If a soldier is a bad apple, he will remain a bad apple and the time will come where discipline is inevitable.
The real point here is your authority; did you keep control of the situation no matter what, were you calm and not emotional and did you end the discussion or did he. These points matter when other troops are watching. Remember: People follow leaders they respect, they dont follow anyone out of respect for the rank.
Good luck.

Discipline

From my humble view, and I got out in 1993, I had the same thing happen while deployed; A PVT said "no I will not do it". I asked him again and explained that although it is no ones favourite detail, that this is mission essential and I only choose those who I know will get the job done". He stood his ground and balled his fists and clenched his teeth. I made the statement that he needs to go cool down and we speak later.
Later in a one on one he simply said he is tired of being in the desert and he is sick of being the private, he could not see the importance of this task for the mission. I let him go with a warning, counselled him and said that setting the example goes both ways; up and down, that he is a good soldier and I too am ready to go home so lets let it go.
the CSM heard all this and told me I did the right thing but at the next smallest detail, I need to lean on him hard.
That night I made the rounds to check the guards on the perimeter, I looked at who was missing and it was the same PVT, fast asleep in his fart sack...needless to say he got an Article 15 the very next day. If a soldier is a bad apple, he will remain a bad apple and the time will come where discipline is inevitable.
The real point here is your authority; did you keep control of the situation no matter what, were you calm and not emotional and did you end the discussion or did he. These points matter when other troops are watching. Remember: People follow leaders they respect, they dont follow anyone out of respect for the rank.
Good luck.

I was an E2, you don't do it! I was in the 82nd back in mid 80's. I saw the decline of respect then.

Discpline