It's already confirmed that Kyul's parents are a red dragon and a blue dragon per her brother
Might be a lie have read enough stories over the years it's basically an intuition now
But when would she have had time to secretly lay the egg and how long would the egg have been incubating for then? Ice monarch was frozen directly in front of Cheolho, isn't a water dragon (unlike Kyul), and decades have passed since then. I feel like there's just too many plot holes to make it work I also don't see any reason why Kyul's brother would lie to Cheolho about the egg being his sister and about his parents
Plus Khan didn't know who Chelho was at first and Cheolho said that he disliked dragons (ch 2), at least initially before kinda adopting Khan and Kyul.
i read several stories over the years where they say dragon egg takes a long time to hatch some even takes 100 years 0r less depending upon authors
I feel like Kyul might be mc's biological daughter with his dragon lover ..