Are you taking drum set, bass amps, etc? Transporting each individual student instrument is no problem….rule of thumb is no gig bags….must be in a hard case or they will get destroyed under the plane. Personally, I refuse to travel and allow my sax to be put underneath. I take a soft gig bag and take it in carry on. Obviously, that’s not going to work with trombones.
As far as transporting the big stuff, I’d look at having it transported via truck. Either ship it, or have a parent drive it there (not sure how far you’re going). I’m sure there are ways to take it on the plane, but if your drive is under 20 hours, I wouldn’t think it’d be worth the hassle…but that’s just me.