Hello and Greetings.
I am a Mexican National (man) who Married a Korean 8 years ago, we met in Montreal, CA, and we got married in Mexico and lived there for around 7 years.
We have 2 kids, all born in Mexico, a boy and a girl. As you may now, in Latin America the women don't change their last name when they get Married, and the kids have both last names of the parents.
Example: Name - Middle Name -Dad's Last Name and Mother's Last Name. (That is the regural way of naming)
We have come to korea regulary for vacations so the kids and my wife spend time with my inlaws (Usually she stays alone with the kids for 2 months, while I have to go back because of my job)
In one of those trips, she decided to Nationalize the kids in Korea.