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

In the late 60’s and early 70’s. If you had an E2 act like an ass an E5 would just assign him to a shit job and he would know why. If that did not work it was down hill from there!

When I was in the Navy, a marine E5 was respected or else. I had many marines who were assigned to me during major buildups of bombs, I was an E5 and I had to tell the Marine E5 what I wanted his men to do. Very easy getting things done.

Every situation is different. How so?
A counseling session slone may be appropriate to see what's eating the soldier as a rehabilitation attempt. Listen, and let the soldier open up and be honest. Married privates in most cases have more problems. Find a solution. If he/she is a habitual offender then you need to lock his/her heels with an NCO witness for article 15 proceedings if it goes that far. A soldier may push his/her luck to see your tolerance and thus continue insubordination. The soldier may have come from poor leadership climate that slowly built up. Stand your ground and set a positive leadership example.
During combat, tolerance flies out the window and can cause the lives of other soldiers!

This is the appropriate course of action. You temporarily disengage so as not to give said Private the chance to degrade your power base any further in front of the rest of your troops.

To everyone else: "Is everyone else, clear on their work assignments for the day?"
Dismiss them to their work assignments.
Once they have cleared the AO, then you get back with said private and lock them up, "PVT Snuffy, Parade, Rest!". At that point either they comply or they do not with said command. It is a lawful order and one that you should be able to cite via the UCMJ as a Non-Commissioned Officer.

If they do not comply and get at the position of Parade Rest which is a modified position of attention and start yapping at the gums again, then you clarify that the position of Parade Rest is a modified position of attention. Hands overlapped in the small of the back, head and eyes straight forward, and mouth closed unless asked a question or requested to respond.

This will tell you if its a personal thing with them or a personal thing with you; i.e. insubordination!

If its blatant insubordination that they are not willing to participate in motivational self correction, i.e. a smoke session or some written assignment/homework as a means of brief extra duty, then you make clear that they will receive a formal counseling statement which will include an improvement plan and referral to higher up the chain, i.e, referral to a Section Leader/Squad Leader who has more experience in such matters and if the Private is continuing non-compliance then he should most likely be referred to the 1SG of the company/section so that they may be refered to other resources prior to a potential evaluation for a Failure to Adapt Discharge. Do not sink to their level. Afterall, you are the one in charge. Defer to higher leadership if they are not willing to assist in their own self conformity and improvement. The longer you allow it to continue or give them the chances to keep challenging you, the more of your powerbase you risk losing in front of the rest of your team.

send Jodi boy on a mission

Whaaaat?

I report him/her to the 1stSgt for office hours. Semper Fi

I had a similar experience, when I was tasked to gather some young troops up to police some grounds ahead of a V.I.P. visit. The E-2 that was defiant and questioned my order explained while he was getting smoked.

I never encountered something like that from an E2, but an E4 yeah, he extra duty for 30 days and 7 days restriction

Tree line immediately. That E2 will accidentally trip and fall, several times, behind closed doors of course. If you don't crush that right away, no one will respect you going forward, nor should they.