Surely it is important for our children to know their Chinese heritage, but we need to be careful not to confuse "heritage" with "culture."

Your racial heritage (whether you're Asian or Caucasian or African American) determines your external appearance. Your culture, on the other hand, is given to you by your people/family. My worry is that if we spend too much energy on exposing our daughters to "things Chinese" and forget "things of our own families" (in my case, Polish and Maltese ... along with French, German, and Jewish)our daughters could come to feel like outsiders because we are emphasizing what is physically different about them, rather than what brings us all together as a family. Your culture is not the same thing as your race. "Culture" comprises the customs and values that your family imparts to you through experiences such day-to-day living and traditional holiday celebrations, and it is the glue that binds families/people together. Furthermore, the immigrant European culture into which I have been acculturated is a far cry from the actual cultural experience of people living in say Poland or Malta. My trip to China a few years back was an eye-opener. Chineses people in China are very different from Chineses people living in Brooklyn, Chicago or suburban Detroit. When our families left Europe in the early part of this century, they continued to grow and change in ways different from the people back home. (If you really want to get technical, they were probably inherently a different kind of people because they felt compelled to immigrate in the first place.)
So as far as our daughters are concerned, I think that we are setting ourselves up for failure if we think force-feeding Chinese culture and language will somehow make them feel more whole or connected. They will be American Chinese (accent on the American). They will not be like older immigrant Chinese who have one foot in China and one in America. Nor will they be like ABC (American Born Chinese), who often live a "double-life," if you will, blending into the American culture with ease, but still immersed in authentic Chinese culture from their China-born parents. Our daughters will be more like the children of ABC: Chinese face, American heart. While I do think a sense of heritage is important, our daughters' sense of identity won't come from constantly looking back to China, it will come from making them feeling at home in our homes, like they *belong* there because they are our daughters.
Take care,
Mary Petertyl