I have a IIe card. As far as I'm aware, you can't simply copy a .dsk file to the ProDOS partition and just use it like a floppy.

You have to use a program such as ADTPro and copy the contents of the .dsk file to the ProDOS partition.

This requires an OS X capable Mac (preferably one with a serial port), a USB to Serial adapter (if you don't have a serial port), and a serial cable that runs from your Mac to the modem port on the host computer of the IIe card.

You then actually boot the IIe over the serial connection into ADTPro. From the ADTPro Mac, you can send it a .DSK file and write to a floppy disk or, I think, the ProDos partition.