The situation is I have 3 characters my lead Cassandra, her ex Mark and her boyfriend Max. Cassandra is Mexican/American Indian. Mark is Korean/German. Max is Mexican/German. Now Mark is convinced Cassandra's twin girls Hope and Katiana are his. But the way the story goes they are Max's. Mark is dragging Cassandra and Max onto a TV show sorta like Maury but called Paternity Nightmares. What I want to know is (for Mark to have some sort of an argument) if the twins where his would they look more Mexican or more Asian?
I suggest you do some creative googling on ethnic traits and genetics. One problem I see is that you don't indicate the relative percentages of each ethnicity, and that would certainly play a role. However, some underlying conceptual problems I see: 1. Ethnic Mexicans are typically a mix of Spanish and Indian. But the mix varies widely. Moreover, there were different tribes in Mexico, each with their own features. 2. The tribes that settled in Mexico (and for that matter all along the Pacific coasts of the Americas) originated in Asia and migrated across the land bridge that once connected Siberia and Alaska, imbuing their descendants with some attributes we would identify as Asian. Moreover, in the first half of the 19th Century, many colonies in the Caribbean and Central America imported coolie labor from China. I don't know how prevalent this was in Mexico, but it was a factor in the region. Hence someone from Mexico could have features that appear Asian. 3. Genetic trait analysis can give us probabilities, but is not necessarily dispositive (as the lawyers like to say). There are recessive traits that nevertheless appear in offspring. Good luck.
Ed did a great job of summing up the considerations. The only thing I would add is that, during the American Western Expansion, Chinese were used (and thrown away) by the railroad in the construction of the first transcontinental railroad. Many of the workers, tired of the abuse, fled southward and it is posited that many of those made it to Mexico and Central/South America. Many of those native CA ethnic groups do display some of what is considered typically Asian characteristics. So it is easily acceptable that some Hispanics might show some of those traits as well. But, as Ed already pointed out, it all depends upon the percentages.
Pffft -- genetics is an amazing thing. You never know what might result. In your scenario anything could happen. Native Americans were originally Asian, having crossed the Bering Strait many years ago. You can have two races mix, and sometimes the children look like a perfect blending of the two, and sometimes they look almost 100% like only one of the parents' race. (Look at the Jon and Kate kids -- they look very Asian, but their mother is white/European and their father is only HALF Korean, and the other half Northern European. Jon himself looks very Asian.) Some Latinos can look very Asian. One of my friends has a daughter from Guatemala. She has had people stop her in the grocery store, insisting that her daughter must be Chinese, and even insist that she looks like people from certain provinces in China.
My sister is tall, blonde and white and her husband is a very dark skinned, dreadlock wearing Jamaican guy. Their kid is a very beautiful toddler boy who looks sort of Indonesian. You can never tell what you're gonna get.