I'd like to talk about the meaning of "household" as it used in the story of Abraham. G-d commanded Abraham to circumcise even "those who are not your offspring", the servants of Abraham's household. For example, Genesis 14:14 talks about Abraham's army composed of trained servants who were born in Abraham's household. These guys weren't literally born in Abraham's house. They weren't even related to Abraham by blood. They were probably the sons of servants that Abraham had purchased and they were trained to be warriors.
There is an ancient Semitic tradition for making someone a servant for life. The master would pierce the ear of the servant which was a metaphor for opening his ears to the master's instructions. Also, blood was a symbol of family/kinship. Abraham most likely performed a similar tradition with his servants. He considered them family. And the covenant (Gen. 17) required him to circumcise these servants.
So how about Gentiles? Do Gentiles belong to this covenantal family of Abraham?