Thanks all for your input, highly appreciated!
I've yet not decided, but I realize that the nobility system might be a bit stricter than I want it to be. But pls keep in mind this is not taking place in the Downton Abbey era, but in our own time. The Monarch recently did set his own position at stake by officially standing up for women rights and gender equality (
Grand Mazaloom Gathering addressing Equality). This once so formal class might have moved a bit onward, birth outside marriage might still be seen as a sin, but they are definitely no longer chopping heads off, although I see that would been a possibility in the old days ;)
I will go a somewhat milder route, but I agree that it is a very serious situation that must be dealt with, anyway. Luckily the Cook's pregnancy is not yet showing, there might be time to marry, but the gossips during the upcoming social season will of course raise anyway. Also, I didn't think of the Butler actually being of higher rank, and mating with a "simple" Cook harming his status, so maybe *he* is the one who should suggest a solution in order to save his own face? If so, it might even be easier for the duke to react milder.
The Duchess pretending having the baby would be an interesting story twist, but it would cause even more gossips: Not only is Duchess of Rossie 67 years old, but she had a "miracle baby"* last year. Yet another birth at her age would probably attract massive interest from the press, but even from scientists and doctors...
(*duke&duchess already had 4 nearly grown up sons, and the game must have made the duchess phone a relative asking whether they should try for a baby, and I must have thought I answered "NO!", but I decided to call it a "miracle baby" instead of killing it off technically, which I have certainly done in other houses. How I wish the game would stop doing this...)
