I reclassed to a 92A and will be going to school. Am I able to take my husband and have him stay with me until school is done?

"Stay" with you? No. You'll be put up in unaccompanied housing on Fort Gregg-Adams like the rest of the students going through 92A training.

As a reclass Soldier, you be given more leeway than an IET Soldier (I gave an overview* on another post) and the guidance to your command is to treat you (as much as possible) as any other permanent party of the same rank/experience in terms of freedom of movement, privileges, etc. IF POSSIBLE, you won't be billeted with the IET Soldiers and will be placed in UAH that is separate from them.

There is nothing preventing your husband from traveling to Fort Gregg-Adams, staying off-post and seeing you when you have time, but I would HIGHLY discourage that because you'll be focused on getting through the 92A training* and the cost will come out of your/his pocket.
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* AIT for prior service and reclassifying Soldiers - https://www.rallypoint.com/answers/12n-ait-for-prior-service?urlhash=8782842
* https://quartermaster.army.mil/ltd/ltd_92a.html

92A MOS-T is 4 weeks at an RTI and 9 weeks at Ft Gregg-Adams. That is a TDY and return course. They will put you up in billeting in a single or shared room.

You would only be authorized to bring dependents if the course was a PCS, longer than 20 weeks.