Oh come on Andy, you have no idea what it's like to be very strongly attached to two different countries. I'm in a similar situation; my parents are Korean, but I was born in Australia. All my life, my identity has been a Korean Australian. Not a Korean living in Australia, not an Australian with Korean background.
I've been supporting the Korean football team my whole life, because I've lived in Korea, I speak Korean to my parents, I eat Korean food etc. etc. That said, Australia is my birthplace and my home, and I've suffered the same heartbreak as the rest of the nation when we (yes, I feel qualified to use the word 'we' when it comes to both Korea and Australia) failed to qualify for previous World Cups.
Tell me, what's wrong with that? Should I be forced to choose one over the other? By that logic, I might as well disown the country whose football team I'd support in the event that they met in an international competition.