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

Well in the old days the words beat your face would be shouted. Not now can't drop soldiers

I agree with GySgt Pepper. You have to act immediately, especially in front of the rest of the troops. As soon as I was told to, "Shove it,", I'd tell everyone else to fall out and turn to. I something close to that happen, but not so confrontational when I was in and I gave them their choice, "extra training", or putting them on report. I had a fellow PO1 stand by (I was the senior E-6 there) and my most senior E-5 as well. Their tune changes a lot when they're no longer surrounded by their peers and having him alone with two E-6s and an E-5 really changed his demeanor. He chose the extra training. So, since it was a Friday, after the work was done, I cut everyone else loose before lunch and he stayed around with me until 1600 and I kept him busy cleaning, watching over him the whole time. The next two Fridays were repeats. Trust me, all his peers knew and he wasn't such a tough guy in their eyes after that.
Like GySgt. Pepper said, let them know that going down that road will cost them dearly. Also, never lose your cool and get into a shouting match, you just lose control when you do.

he would wish he had never been born

When I was a Sgt borderline hazing wasn't looked down upon. I would kick him out of formation and have him do push-ups until the battery gunny came out. After formation I would grab another NCO and we would tag team him and just blast him and put his ass on duty for a couple weekends. If it happend to me or another NCO again, disciplinary action through the 1stSgt would be next.
Now there is more paperwork involved and treat them kind and understand their needs and support their feelings.

Write him up for insuboardination

Quickly. Either in front of the formation or just the private and the squad leader. Either way, the private WILL understand any failure to follow instructions WILL BE SOLVED BY THEE UCMJ!!!!

A few weeks in CCF will curb that piehole. This is old school thinking ('84-'93). There where dire ramifications if you showed any disrespect.

Well, in my days in the U.S. Navy, this young so-called man would have been scrubbin' the deck with a toothbrush for the next six months. That I think would be a good start !!

PFC Shitbird needs to remain while the rest are dismissed. I need to explain that his life just changed and I am taking a personal interest in his career. He would then be asked to follow his orders and it would be explained that all of us need to work together and no job no matter how demeaning is unnecessary to our mission. I would add some supervised extra duty and a written report on Article 91 and how he violated it.

An E-2?? That happens?? Does he still have teeth?? I know I know not in today's cuddly military.