357 poker question

Does anyone else here play 357 in their dealer's choice games? I had a question about the three-card round. I had just taught my family how to play it and we were on about the third hand when my dad showed a pair of aces down against my cousin's JQK, which he claimed was a three-card straght. He had assumed that the round of three used a ranking system like the three-card poker or three-card monte casino table games. When I was taught the game over a year ago, three-card straights and flushes in the three-card round weren't mentioned. What should my ruling have been?