First, I agree with Yrma that's it's ironic to see a White person spending so much time attempting to explain why her definition of "race" is appropriate. I also find a lot of inconsistency in your position, but that's not the essence of my comment.
Acknowledging ethnicity is one thing, but to say that it's a "pride" thing suggests that there is an importance attached to races. The fact is the word pride implies superiority, which I find disturbing. This logically means that people should choose to define themselves by races out a sense of recognizing the "better" racial aspects of their background. Otherwise, what's the point in saying that it's about pride. I see no pride associated with race, only as a description that society chooses to impose on the person.
I believe that race has ABSOLUTELY NO INFLUENCE on who you are as person, unless you are a black person in America. Then, you are defined by your blackness, whether you are dope dealer or the President of the United States. For black Americans race can be a source of motivation because you understand how much you must overcome to have a measure of equality freely given to others by virtue of their race.
Both of my children are the products of two races, Black/Asian and Black/Spanish. I will always refer to my children as black as they have features that identify them with the Black race. It's much more important for me that they understand how they will be viewed by society and deal with those realities, in spite of any ethic description. For me, anything else is a disservice and creates a false sense that they might get "credit" for being part of another race. Of course they understand that their parents are of different races, but it's irrelevant. I care much more for their psychological well being and instilling in them the knowledge that they can't forget their blackness, because society certainly won't forget it.
In fact, arguably, people who choose to identify themselves as "bi-racial" could be subjected to more disdain, if part of the identification is with the White race. Many White Americans would find such associations to be offensive because they see something different. But, this is the state of racial politics in the United States today. So, I choose to be a realist.