I've got a bunch of parts that are mouted to a single bracket, and I would like to move the bracket and everything on it into a different assembly. Is there a way to do this without re-constraining everything?
After a first read-through, I would say save the bracket and parts as a subassembly and then add it to the other assembly.
Alternatively, you could try using the RESTRUCTURE command to move the bracket from one assembly to the other. You may need to re-contrain the bracket, but the parts assembled to it should follow without any problems (assuming they are assembled to the bracket explicitly)
try to use it in addition with the reference control because when you use the restructure command many times in an assembly you may create unwanted references which will fail regeneration if you make a change or you try to change-edit dimensions of a component in a wrong assembly.
ptc says that you dont start designing a project until you get the right information
so try to make a draft scheme of the structure of your assembly and then assemble the parts
restructure is good command for fast (but dangerous) bom changes