It would seem responsible for RCI to wait until your planned cruise reached its final destination before producing this type of document. They have to be able to truthfully say that passengers X, Y and Z did not embark on this cruise at any point. Your child was denied boarding last weekend, IIRC, so I am not surprised that no documentation has been produced yet. Hopefully it will come along quickly now that the ship has disembarked that cruise.
Keep in mind that cruise cancellation departments and insurance have been super busy dealing with COVID 19. They may have had to add extra new personnel to deal with this.
A few years ago my father passed away after the final payment date of a very expensive cruise on a different cruise line. It took months to get a refund through insurance, and we had a death certificate. (I’m not sure that his wife was ever refunded - insurance through it was perfectly reasonable to expect a
new widow to go on a 3 week cruise one month after her partner passed away).
I hope your kid kid is feeling better, and you can get some satisfaction shortly.