Wobbly side box

Raise the box up to the top of the mounts on the trailer frame. It will stop the bouncing. You don't need to mount the box to the frame but the angle iron is is not strong enough to hold the energy from the box movement when it is past the trailer frame like it is. There is no way to really absorb the energy unless you doctor up more bracing. When it is mounted higher, the angle iron up against the frame with the box mounted will take the energy away from the box.

if you remake the mounts, use 3 inch wide angle iron with a 3 inch wide flat piece.

 

Bottom line, you have too much leverage and not thick enough bracket material. Its going to flex.

Personally, Id have used 3"x1/2" angle.

 

My trailer is different obviously, not sure what size brackets either but atleast you can see it.
Trailer dealer mounted it.

 

Looks good, always like seeing someone do something themselves and taking a little criticism gracefully along the way and implementing it. That said, I think I'd mount a mudflap between the box and tire