When did "Kim Jongkook & Two Kids" disband?
So, they never technically disbanded. I think when Monday Couple was formed, Kim Jong Kook and the 2 kids kind of stopped being a thing.
While the 3 of them have been on teams together a lot (check our lists page for all the episodes), the three were only ever on a team by themselves in episodes 12, 16, 18 and 25 (kind of surprising considering what a lasting impression it made).
(gif is from ep 149)