If you think about it, about it, a little over a hundred years ago, the Western United States was pretty wild. 

Except for the Natives who lived there, the land was relatively untouched. When the United States bought the remainder of what is now the US, and everyone kind of wanted to know what we had purchased. Slowly over time, pioneers and settlers started moving West, beginning new homesteads and towns in this unexplored region. 

This brings about that idea of Children of the West. 

I have lived in California my whole life, and I feel this identifies with me. But I have family spread all across the country, so where do I actually belong?

Honestly, I don't think it actually matters. You can be a Child of the West if that's what's important to you. Our ancestors may or may not have been pioneers of the West. But this is where I (you) am now. 

So being a child of the West isn't based on facts, or where you were born, or even who your ancestors were. It's a personal identity, and you deciding where HOME is.