"All Israel" here is a generalization that means the capable men of Israel who represent the rest of the people by a synecdoche. Alternate translation: "when all the leaders of Israel heard" (See: [[rc://en/ta/man/jit/figs-synecdoche]] and [[rc://en/ta/man/jit/figs-hyperbole]])
"Israel" implicitly means the northern ten tribes that rebelled against Rehoboam. Alternate translation: "king over all of the 10 tribes of Israel" (See: [[rc://en/ta/man/jit/figs-explicit]])
This double negative emphasizes that the tribe of Judah was the only tribe that followed the family of David. Alternate translation: "The only people who followed the family of David were the people of the tribe of Judah" (See: [[rc://en/ta/man/jit/figs-doublenegatives]])