He will have orders when he leaves BCT. He should have a statement about his dependants on those orders. If not, the orders will have to be changed when he gets to AIT. Which takes time.
IF you join him at AIT, you must understand he is UNAVAILABLE during worktimes. The Army is not a 9 to 5 job, although some days he will be able to come home "on time", other times he will have to go in earlier than 'usual' or 'come home late'. Or go in on a Saturday to sit in a classroom. He will not like this and neither will you! Bitching about it to him will not help him.
He will not be able to just stay home to watch sick kids, to take you to the store or leave for emergencies- even bigtime medical appointments.
AIT SUCKS because you're still shackled down with what is called "TRADOC" (tray-dock, Training and Doctrine Command). Yet if it's a long AIT (which it has to be for you to move there,) it will begin to seem like a boring regular job. He needs to stay focused and just get it done so you can go to your "first duty station" and be free of that mess.
At my AIT my wife moved to Fort Gordon with me. We had one car, sometimes I took it, sometimes she dropped me off. I remember several incidents where she had to wait around a few hours for us to get released for whatever reason. I got a phone call that she had been in a car crash. I had to wait until the end of the day to go with her to get a rental car and see our car.
I taught AIT for a year, and have been in the army 12 years now. the Army has been quite the experience. If your husband DOES WHAT HE SHOULD, as well and cheerfully as he can, the Army will take care of him and you.
But I have seen other families where the Soldier just doesn't like doing what they are supposed to- they don't get promoted, they have problems with their supervisors, so the boss is less willing to cut them any slack or work with them if there are problems or emergencies.
welcome to the Army family and good luck to you!