2 Computers 1 USB Device (circuit help)
5 options:

1, use the usb switch you mentioned. Or one that can also switch power. That's exactly what they were designed to do.

2, use the second usb interface on the NXP device, and disconnect from the first usb interface/RPi when it detects a connection.

3, use both usb interfaces that your microcontroller has at the same time, one per host. Code the product to respond to only one control interface but spit data at both.

4, use the RPi as a middle man, not having the "real" (what is real ) pc connect to the usb device, but to the rpi via network, or the RPi usb peripheral connection. 

5, use an alternative to usb, like bluetooth, ethernet, or wireless. Frankly, that microcontroller can act like a real pc as well.