Can I Defer drill because wife was in school before I came down on orders...?

Have you tried just asking for a deferment? You just get some supporting documentation, a letter from you explaining that it will create a hardship and that you're not trying to delete - only defer, one from your commander saying he supports it, and then send it on up on a 4187.
You should definitely talk to your branch first. Infantry branch is really easy to work with, just difficult to get ahold of at times.

You can decline Drill School, that comes with a bar to reenlistment.
You can call Branch and the Course Manager or OPS NCO at Drill school, let them know why you need a later date. This will require a 4187 with a signature from your BDE CDR, so I would let your chain of command know what's going on and why you need to do this. Worst case scenario, you get a cheap AirBNB room and pay two rents for a while, because you can defer the actual PCS contract movers for up to 180 days. If you are in on post housing now, that deferment will also require a BDE CDR signature.

You can always defer/refuse- tho it could kill a career. 2. It only takes a phone call to Branch (when they answer) to explain the problem and possibly get deferred.