These two lines are parallel, with "Israel" and "the house of Jacob" meaning the same thing and "Egypt" and "that foreign people" referring to the same people. (See: [[rc://en/ta/man/translate/figs-parallelism]])
The word "house" here represents the family or descendents. The verb may be supplied to this phrase. AT: "the descendants of Jacob departed from that foreign people" (See: [[rc://en/ta/man/translate/figs-metonymy]] and [[rc://en/ta/man/translate/figs-ellipsis]])
Possible meanings for "Judah" and "Israel" are 1) they refer to the land. AT: "The land of Judah became Yahweh's holy place, the land of Israel became his kingdom" or 2) they are metonyms for the people of Judah and Israel. AT: "The people of Judah became those among whom Yahweh lived, the people of Israel became those over whom he ruled" (See: [[rc://en/ta/man/translate/figs-metonymy]] and [[rc://en/ta/man/translate/figs-ellipsis]])