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

Just as you said. Keep the Pvt and Team leader back and dismiss the rest. Then you explain the Pvt shitbrain how this works. If he continues to mouth off, you issue him a reprimand, follows by additional details plus the one he was given. When he is through you bring him in and sit his ass down and explain the Proper way to address his supervisor in the event he has a complaint or a problem. Depending on his response, you tell him to hit the hay.
Pvt shitbrain got through basic somehow so he understands what it is like being in the military. He isn’t in High School now and he isn’t going to get credit recovery, or make up seat time, or in-School suspension. Those days are through and I’m sorry as hell his high school and family didn’t prepare him for the job he voluntarily took.

Well son you are in a heap of trouble. Insubordination gets you an all expense trip to the brig.

Again, a subject of what to do with a sever dipshit in your unit? Another take would be to send Pvt/Amn Dipshit with a Letter of Reprimand to see the executive officer with a recomendation for non judical punishment. If the officer has seen enough paper work on pvt/airman dipshit, he must approve an Article 15 hearing. All the evidence of disrespect to superiors, not obeying orders must be presented. When sentence is passed, dipshit must go to jail. Then his time is served, show him the gate out under escort, usually with two very large security personnel. In generall, get rid of the bad trash if it won't adhere to the military way.

The PV2 will be assigned that duty plus any extra duty that needs to be done such as scrubbing toilets, garbage cans and any other nasty duty I can imagine for the next week. They will perform them without complaint immediately following a counseling statement where I explain that failure to perform said tasks will result in referral for a company grade Article 15 for failure to obey orders.

you tell them is is a lawful order. If they refuse, you take it up with the PLT SGT or better yet 1SG. Failing that, well the CO for Article 15. Use the chain of command 1st. the 1SG has much more experience and can handle it without resorting to UCMJ. But if they insist on being dirtballs, oh well.

I call them into my office and have a heart to heart....Someone who does this there is an obvious reason for this behavior. I also know that I could have made an example out of them by humiliation in front of other's and they might not do the same...but I feel this is not the answer. This could be a cry for help. But counseling is in order for sure.

Looks like Kp and no furloughs until he she shapes up.

Depends on the nature of the situation. Did the PV2 say something that was taken out of context by the leader - was it meant to be disrespectful or distasteful? Has the PV2 recently experienced an emotional trauma? Are there any issues of the PV2 being harassed, intimidated, bullied, or hazed by the squad or platoon when leaders are not around... or is a leader abusing the PV2? Does the PV2 have external problems going on that need to be factored into equation... alcohol abuse, drug use, family stress, marital problems, new baby on the way or already here, sleep disorders, adjusting to new medications that cause a chemical imbalance, hormonal imbalance, hypoglycemic issues, thyroid problems, blood pressure problems???

We are all human, and true leaders in the military learn how not to respond emotionally or erratically in response to a subordinate losing control of their emotions, composure and professional demeanor.

As leaders we are given the charge to lead, discipline, and train - but we are also given the responsibility to care for our troops and their families, and to investigate sitautions by asking the 5Ws and How? If we only react instead of being proactive, seeking answers by asking questions to investigate the real cause of the problem, and if we are too lazy to use all the support and resources we have at our disposal - then we are not being effective - because we are not being a solution - rather we are simply adding to the problem. I always believe by praising in public and admonishing in private. My ego was never bigger than my rank or position, and I could handle a PV2 losing themselves for a moment without it affecting me or my ability to maintain command and control.

So, find out what the real situation is, find out which leader within the CoC the PV2 is willing to speak with - to include the Chaplain, and work on what the real issues are. If the PV2 still needs to pay for it - then make it fair... in time this PV2 could one day be the next SMA or 4 star General ---- would we want that person to be the kind of leader I just spoke about as they rose through the ranks, or a hard-ass who could care less amd is abusive and slips through the ranks becoming a toxic leader like we have experienced in abundance over the past 20+ years in our ranks? Remember, we are not leading Privates, we are training Leaders! Give this PV2 a mission or area od responsibility (within an area they have an interest to excel) - assign them a mentor, and have them become accountable to more than just himself - or herself.

Lastly, counsel every 30 days on paper - setting attainable daily goals, weekly objectives, and monthly expectations - and find something to praise them for each day and at the end of each week - and if they come up short on something, take time to teach, coach and train them (if not you, then your subordinate leaders). Good luck!

P.S. - I was had a PV2 who was underage drinking and crashed his car off of a 7000 foot mountain... kid lost his brand new Mustang and almost lost his life. I could have discharged him... that's the easy thing to do. He was a good Soldier most of the time (a knucklehead other times - but that comes with age). After his rehab from surgeries and Article 15 punishment + 90 days confinement with extra duty (again after full physical rehab)... I didn't judge the PV2 harshly and I gave him room and time to bounce back. I encouraged my subordinate leaders to mentor, coach and train him. This kid ended up saving the lives of 2 kids from a burning apartment fire a year later, promoted to Sergeant 3 years later, performed flawlessly in combat, and then later was accepted into the Green to Gold program, where he went on to earn his degree and commission. Now he leads troops! Just something to think about as you consider your options.

Follow the guidelines set forth in FM 22-102 following formation.

In my day we would put that idiot in the mickey mouse gang, and if that didnot change his attitude then muster his ass out with a bad conduct discharge. And that would happen in just 2 days time.