Pic of fixed half attached.
What do you mean by "float"? The bracket is welded to the cart and the caliper slides on. One half of the caliper is on the left of the disc, the other on the right. The right side of the disc is the side that has the lever attached to the brake line.
I believe that I mistakingly and quite stupidly switched the plate with the pad when reinstalling the brakes last week. Instead of going disc, pad, plate, caliper shell; I did the following: disc, plate, pad, caliper shell.
I believe the pressure applied to the center of the pad is what made it split. (the crack originates dead center). the pressure was applied by the domed piece that moves in and out of the shield/pad chamber. In addition, that same chamber was filled with grit from what seemed like pad debris. That's why I think it broke.