A more specific term for "ancestor" can also be used, particularly if the word "ancestor" would only be used for someone who lived before one's grandparents. AT: "Josiah was a grandfather of Jechoniah"
"when they were forced to move to Babylon" or "when the Babylonians conquered them and made them go live in Babylon." If your language needs to specify who went to Babylon, you could say "the Israelites" or "the Israelites who lived in Judah."