I want to connect an existing desktop to my current wireless router. My daughter's laptop has given up the ghost and I'm hoping to use her PCI card for the desktop. Can I connect it to the desktop via a PCI card reader through a USB port?
You must mean a PC Card (aka PCMCIA or CardBus) reader.
They do exist. Linksys, Netgear, etc. sell their own for about US$40, last time I looked, and you can probably find generic models a bit cheaper. However, all the ones I've seen install in a PCI or ISA card slot in a desktop machine; they don't make USB variants that I'm aware of.
FWIW, you'll spend the same or less buying a new Wireless USB adapter for yourself than trying to find an adapter to make use of your daughter's notebook card. You can find new 11b USB adapters for US$20-$30 (after rebates).