Does an E-5 who is reclassfying stay with the Privates or stay with the wife?

If the duration is less than 6 mos, it’s a TDY and you’ll be living in the barracks. Reclassing to 19D, you’re looking at 4 mos for the whole OSUT or 6-8 weeks for the AIT phase of the training.

Depending on when you get there and the number of reclasses, you may be mixed in with the IET soldiers or you may be segregated.

When I reclassed, I was provided w/ a permanent party barracks room; it was away from the IET barracks. As far as bringing your wife along, that will be highly unlikely. The school has to be a certain length to be considered a PCS move. I am not sure of how long it has to be, but I have read something along the lines of 20 weeks or longer.

When I went through AIT for 13F we had a prior service 13B E-4 which was in another wing separated from all trainees. Had liberty and such after working hours/ weekends.

The 'RULE' is NCOs are not billeted with privates (especially trainees) so you may be be given an NCO room (probably doubled up) on the bottom floor near the CQ or you may be doubled up at a nearby BAQ.
It won't get you out of supervisiing any details involving the other soldiers but you will probably be the supervisor. You should be ready to instruct the trainees on proper cleaning of toilets, sinks and showers plue the sweeping, mopping, waxing of hallways and common areas.
Enjoy!
OR
Maybe, since you're married, you should check with the training unit's CSM/1SG. Call ahead and explain your situation. Perhaps your current CSM/1SG can call to discuss it. There maybe an E4 Mafia BUT there's the NCO Brotherhood too.

If you BCT/AIT is under 20 weeks, then you stay in billets. Whether that is a NCO room or what is up to the school.

Those are both TDY length courses, you will not bring your family. Whether the school mixes you in or separates you is up to them. Typically, prior service are separated, but that's up to local policies/commanders/Cadre.

Where you stay depends on the length of your AIT. Works like this. Under 20 weeks you are not authorized BAH so you will stay in the billets regardless of rank. You will not/should not be billeted with privates however. You may get your own own or be billeted with another sergeant if there is one.

For AIT's that are 20 weeks and over you are authorized BAH BUT, you won't be living with your spouse until you pass a specific phase in AIT. At that time then you can move in with your spouse.

That will depend on how long your MOS is and if your school allows you to move off base. You won’t be in the same barracks as the brand new Soldiers from basic. They should have a separate barracks for Soldiers who are reclassing. I think your MOS has to be 20 weeks or longer to even be able to live off post