Will my wife have any kind of a break between BCT and AIT?

It depends If is she is going to be a Reservist or member of The National Guard and will be attending college soon after completion of BCT she can opt for a split option in her contract to complete AIT the following Summer. The only time an active duty contract Soldier gets a break from Basic and AIT is Christmas Exodus or emergency leave. In a nutshell only the above listed exceptions get any break between Basic Combat Training and AIT, The vast majority do not.