fatal error: avr/io.h: No such file or directory
The Due is SAM architecture. avr/io.h is specific to the AVR architecture of the Uno's microcontroller. The compiler will not look in the avr tools folder for that file and even if it did it wouldn't help because that file is not compatible with the SAM architecture.

This error indicates that part of the code you're attempting to compile (probably a library) is AVR specific. You will need to either port that code to the SAM architecture or find an alternative that is already compatible with Due.