Solution 4, for the future drama that would bring. If the mother isn't showing yet, a common solution was to marry. People might still notice the shorter pregnancy and gossip, but that would spice the story up, so I count that as a plus. The butler would of course lose status and probably his job for marrying below his station (except you are not that strict and treat all servants as basically the same class).
If the duke and duchess have relatives, those might take advantage of their peers being too soft on the butler and cook, maybe weakening their status among the other nobles by always pointing this out.
