@Arvadiel no from what I've taken from it Illegitimate children die from being killed in the crib by their Emperor fathers. It should be understood that these are the first Illegitimate children in the Royal Family to not be instantly snuffed at birth. So they have no idea what's going to happen here because no Emperor has allowed "tainted" offspring to survive.
Honestly surprised. I assumed the reason the king retrieved the twins was because they were meant to be back ups if the prince (or princes since alex is the second) kicked the bucket