my father immigrated to Germany when I was very little, I grew up there went to college, moved around Europe for a couple of years and then came to the US. The "Integrate" part is not all that difficult. When in Rome, do as the Romans do. And if that doesn't suite you stay the hell out of Rome. No matter where you are, you have to learn the language, adopt the local customs, follow the laws and participate. Don't go insisting on how "Different" you are. If you can't appreciate the culture of the place, you've picked the wrong place. I managed to fit in, repeatedly, without forgetting my roots or loosing my Identity. But then again, I didn't move to Saudi Arabia but places that were compatible with my upbringing.
And having multiple ethnicities in a family is not an issue. I my extended family we have Mexican, Korean, Lebanese, Russian, German, Swedish, Finnish, Albanian nephews. They are all cousins and get along just fine. In fact, it is rather convenient to be connected to so many places. You got a place to stay no matter where you go.
And it also gives you an insight into what's going on in the world. And you can't help but notice a certain anxiety. Even in places where the economy is humming and life is easy. A lot of things are in flux. For the greater part the places I've mentioned have improved dramatically over the past 20 years but now there is a feeling that we are running against a wall. Yes, life is good for me here in Texas, my lazy ass can make an easy leaving by doing a bit of planning, pulling resources from a competitive, and cheap, global pool, and applying a hefty markup. If it weren't for globalization I would be forced to do real work. But the situation is different for the kids. Even in places where there are jobs, good jobs are rare and investing much time and money in education has become a risky investment. What's IN today is already OUT tomorrow. It is becoming increasingly difficult for young people to find their place in this fast paced environment.