How to transport bulky things on a bike
This is quite tricky, given a trombone is not a nicely shaped instrument. You can try some larger racks, or mount some plywood or something to a smaller rack to try to get a more stable surface to carry the trombone (or be able to build something that allowed carrying the trombone like a pannier), but I doubt it will be very good, especially with all the additional stuff you want to carry. I do know some cellists who have strapped their cello to their backs and ridden (somehow), but I don't think it was a particularly stable or safe solution.

The real solution I think is for you to get a cargo bike. One thing you might want to try is to do an Xtracycle conversion - the Freeradical was a kit which allowed you to extend a normal bike into a cargo bike (but is currently not being sold -- you may be able to find an existing bike/kit somewhere thoguh). Unfortunately, cargo bikes like the Surly Big Dummy and what not are not exactly cheap (and are not normal bikes), but your use case is pretty much what the cargo bike was designed for. 

An example of a Freeradical conversion is: 



and a xtracycle carrying another bicycle



Note that there are other styles of cargo bikes out there, like the Civia Halstead: 



Another option is to throw the trombone and what not into a small trailer, such as one of those children's trailers like this (a cheap one will be about 150 bucks): 

 

or attach a regular bike trailer like the Surly Ted (about 700 bucks for this model, but there are cheaper ones):