These folks are running a business and have to protect themselves so I understand why they would ask for additional information when shipping to a different address than the CC billing address. With that said, I too would be very hesitant to send anyone a copy of my DL with my credit card. If anything, I would just use Paypal - if they accept it that is...

Some time ago I placed a relatively large order through Horizon Hobby and put the shipping address as my work address as I do with many online purchases. Within a day or two I received an email saying that my order had a problem and couldn't ship. When I called them, they asked me to contact my CC company and put my work address on file with them as an authorized ship-to address. I understood the precaution, but I wasn't in the mood to go through the credit card company's talking menu system so I cancelled the order and placed it with another reputable online company who promptly obliged and shipped my order