Coupling SD card with SD to USB converter

I'm working on a project using the sam3x8e from the due. I'm saving the data as a .csv on an SD card. I would like to be able to access the data as a mass storage device through a pc without having to remove the card. So, I had an idea: why not just take an SD to USB card reader and solder all the pins from my SD breakout board to the pins on the card reader. Surprisingly this works, with the restriction that the card reader cannot be plugged into the pc while my device is running and vice versa. I think this is because I'm essentially trying to drive one slave device with 2 masters that aren't on the same page.

So, here are my questions:
Does anyone have more information on how these sd to usb converters work? I'm using the one linked below, and it conveniently has epoxy right over the pcb where it's labeled U1, so I can't tell what kind of chip it's using.

Is there a way I can tell the sam3x8e to stop trying to control it's spi port? If I can detect when the usb is plugged in (easier problem) then I can tell the the sam to "let go" of the pins for use by the other device.

Any info helps, thanks