It all comes down to how the 3rd question is worded. This will determine which answer is correct.
I've always seen this question read "The oldest kid has red hair"... So it would have to be 2/2/9. This makes the final answer more obvious because the "oldest kid" HAS to be the nine-year-old. 1/6/6 does not work because it's "kid", not "kids" (therefore two 6-year-olds don't count).
In your case, I would have to agree that 1/6/6 would be the answer to "the youngest kid" question. I just assumed it was the same question so I thought it was 2/2/9.
But the little variation in the third question threw a wrench into things.
I think you should say "youngest kid", and not just "youngest". This will also specify the NUMBER of kids involved which makes all the difference in finding out which is the right answer. If you just say "youngest", then someone can argue (like you have) that even among twins there's a younger one of the two twins.