How does one remove this cap without killing it, the trim, the seat, or one's self? Thanks

 

It's a press-on fastener, similar to the ones that hold the wheels onto kid's little red wagons. Use some sort of fork tool (think door panel fastener removal tool) and wrap it with electrical tape.

 

Good advice. I got a kit of two of those and a pair of spatulas/ handles things that lever when you press. It came off, as did the rings holding the frame to the rod. Halfway disassembled now, will resume in a bit. Thanks.