I see error in this statement. It supposes that the 10 sons of Abraham that were not Jewish were no longer sons of their Patriarch Abraham. The origination of the Jews was the seperation of the sons of Jacob after Solomin's stupidity (they called him wise) in taking foreign idol-worshipping wives.
The tribes became the Southern tribes; Judah/Benjamin...the Jews and The Northern 10 tribes; Ephraim or the house of Joseph. These were the ones who were scattered into the world, those that Jeremiah said would be searched for someday as fishes. Those that Jesus sent his disciples after saying they would be "fishers" of men. (Jeremiah 16) Those scattered into the world were "Israel" because they were still sons of Jacob..... these are the "Gentiles" A specific group of people with specific heritage in Abraham. Hence the fact also that the word Gentiles is usually always capitalized..... it's a hidden clue.
What you are saying is just not correct. If you do a search of the word "Gentiles" in the NT, for example, you will find multiple passages where what you say simply cannot be, and not one passage where it must mean what you say. I am certainly well aware of the division of the kingdom and the later dispersion of the northern tribes, but those dispersed Israelites were not the same thing as the "Gentiles."
Your assertion that the Diaspora equals the "Gentiles" is an unusual, if not unique, view. How did you come up with it, or where did you get it from? Do you have any Bible passages or other evidence to back up your claim?