In answer to the question, you asked are we the children of Noah and his family of three sons and their wives?
The answer is yes, we are descendants of our forefathers, Acts 17:26. If the earth must start all over then Noah and his family are our ancestors, Genesis 9:1. Mostly because this is the history of all mankind as recorded in the Bible.
Are the ancient ancestors of the Biblical flood an inbred race?
The answer is yes since people are all flesh and blood, even if it were true that racial differences does not mean impurity. It means that the genes of humans have always had a variety of facial color because racial differences are a genetic abnormality that occurs without salvation. So, people simply give birth to different races in the past, but as the world separated into national racial countries the same genes continue dominantly among ethnic countries.
Another point is that is the Biblical story of Noah’s Ark is an art of fiction and is just simply the writings of God. The Bible is stories made up that displays God and his powers or rather stories made from the God of the Bible named Jehovah, Psalms 83:18. The title God is what the creator in the Bible is. All the stories of the Bible are said to be the power of the writing literacy of God's personal name Jehovah.