For whatever it's worth, my mom is American (Irish, Danish) and my dad is Mexican (Native mixed with British, Italian, Spanish). To them, it was very important that I never say that I'm half anything. I've always said, "I'm Mexican and American." Here in the U.S. that invariably leads to a discussion of the ancestry of my American family, but it rarely occurs to anyone that my Mexican ancestry is just as mixed.
It's interesting that my husband's family, which considers itself to be "pure Lebanese" also has stories about when their ancestors arrived in Lebanon from Yemen.
So, really, is there any culture that is really "pure"? I doubt it.
But as for what my "culture" is--I was mostly raised in Mexico within a mixed Mexican and American context. And the American part of that came from all over the U.S. from all sorts of backgrounds. But what differentiated it from Mexican was the value placed on personal independence and ingenuity. The Mexican side placed more value on obedience and family reputation. So I learned a bit of both, if that makes sense. I learned how to be respectful and obedient in social situations while still maintaining an independent sense of what I will do with my life.
There is a huge difference between the questions "what is your ancestry" and "what is your culture." So I would say that in your case, as in mine, your daughter is Indian and American. If that discussion leads to her American ancestry, then it's good she'll know all about that, too!
BTW, my parents have found a lot of fulfillment in travelling to various parts of Europe looking for both of their ancestral origins. They've read all about my mother's Irish ancestors and traveled to the part of Ireland where they're from. And they've read all about my dad's Italian and British sides, and found a castle in Italy that bears the family name. It's a neat thing they've done and passed onto us, and I hope to pass on that curiosity to my kids as well.