Communication between a USB/serial device and an AVR (atmega/Arduino) microcontroller
If your device shows up as a CP2013 when you plug the device into a computer's USB port, and you want to replace your Computer with an Arduino, then that isn't really easy to do, or generally possible. The methods you mention in the question have to do where the AVR/Arduino is the device, not the Host. 

The device already has a USB-UART converter embedded inside it, and only shows you the USB side of it. This means that your arduino needs to function as a USB host. Functioning as USB host is not straightforward. You need to set up a USB Host/Hub controller, and figure out how to handle enough of the USB protocol stack to talk to the CDC compatible USB-UART device. Using a USB OTG Host controller may be marginally easier, but still nowhere close to being trivially easy. Your best bet would be to see if you can bypass the CP2013 on the device and access the UART lines directly. This may not always be possible. If the CP2013 is actually some other piece of hardware or firmware masquerading as a CP2013, then you're fresh out of luck.