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

First, I’ve never heard of a Senior E-5 so E-5 will do. If an NCO gives a direct order and an E-2 refuses then the counseling and paperwork begins. Tracking everything is essential in today’s environment and when rules or regulations are broken there is a process for that.

I had that happen once but the guy was an E4 who somehow arrived at the conclusion that he had special privileges. Basically I EXPLODED right there, in his face and told him in no uncertain terms what I would do to him if he EVER spoke to me in that tone or manner again. Sure it wasn't exactly 'professional' demeanor (especially in today's military) but it damn sure was effective, the dumbass practically shit himself and fell all over himself apologizing and excuse making at which point I told him to go get himself together and then report back to me when he had regained his self control. We set things straight between us and for the remainder of our time together he was a good troop.

What the hell has happened to the Military? In my day, if an E2 said anything other than "yes Sgt" he would go to the firing squad.... ok, not quite but damn close. I'm assuming this really happened.... Seriously, what has happened to our military?

Frankly this is not a reprimand in private situation as cpl P mentioned. Complaint and insubordination was public making it seem to the rest of the squad that assignments are optional and that disrespect will be tolerated.
1st inform the insubordinate E2 of the consequences of disobeying a legal order, in front of the team. The reason to do this is one, to have multiple witnesses of the incident if needed in the future, and also impress on the rest of the team that you are handling this within regulations and will be handled the same way if any other individual feels the need to be insubordinate. 2nd- Time for some team motivating activities or restrictions to allow the team to assist in adjusting the error of the the E2's ways. Squad punishment has a way of impressing the right attitude on problem children. Lastly, if there is not a conciliatory response from the E2 move to formal article 15 ( or similar) punishment. Zero tolerance for this type of BS since the next time he refuses could mean the safety or lives of others. The military is a dangerous business and not time to let individuals think they run the show

I agree with the praise in public, punish in private EXCEPT in the field or on deployment. Set the expectation of this difference when they join your team. In garrison, excuse everyone except the mouth & their squad leader. Junior enlisted will get what they need and their peers will know what is coming as the example they need. In the field, snap their head back with quiet fury and rip them and their squad leader a new one after the mission. In garrison it degrades morale: in the field it can get people killed.

Well... I’d get that shitbag to grab his e-tool. Because I NEED to know he knows how to dig a fighting position correctly. Then I’d make sure he knew how to dig a second one correctly then a third, because you don’t really know how to do something right until you can do it on your own correctly at least twice, if they refuse then it’s time to start paperwork. No second chances let him be an e-1. F@&$ him.

No problem. I call them to the position of Attention and then march them to the 1SG's office. I leave them at Attention while I explain their transgression to the 1SG. I feel confident that the 1SG will assist them in seeing the errors of their ways.

Pull that maggot right out of formation and take him/her behind the paint locker and express your leadership skills until that little shit shows respect. The military is no place for coddling momma's little spoiled and selfish brat. If that military personnel behaves like that, someone will die in a war type situation in the future if that situation is "ignored," not to mention that leader will lose the respect of everyone currently and in the future under his/her command. Think about it.

Article 15. As a non-commisioned officer I expect immediate compliance to all my orders. If you think you are in a democracy in the military you might just as well learn now that is not reality. Stripe losing time, period.

I would offer them two choices, just as my old 1st Sgt would do. I would tell them this is an order. You can choose to obey the order or you can choose to ignore it. I would then tell them if you obey the order, everything will be fine. If you choose to ignore the order or disobey the order, I will recommend you for an article 15. I will then explain to them that once they have been found guilty at the Article 15 hearing, I will make sure they are aware they will be found guilty at the article 15, they will suffer loss of rank, forfeiture of pay, extra duty and restriction to post. I will then ask them, what will it be, doing what I order you to do right now, or suffer the consequences later. I have not found anyone yet stupid enough to opt for an article 15. Should they have ever been stupid enough to opt for the article 15, the way I would ensure they would be found guilty is by calling another NCO over to witness me give them this order. Having a witness ensures that upon the hearing for the article 15, it won’t be my word against theirs.