I could only try to excuse that with the fact that she literally came in with her mother, who, well, isn't THEIR mother, but looks extremely similar to her. Therefor a child of said woman who looked like the late Duchess would also look similar to their mother naturally. Since the father didn't have an affair, and as long as that sleeping lady was accepted as her mother - which nobody had any reason to doubt at this point - she could not possibly be his daughter. That, in fact, is common sense, though it's not spelled out, so I'm not sure if the characters use that common sense or if the story didn't actually realize that fact.
But yeah, as a matter of fact, not believing Bebe is the Duchess' last born child is common sense. So, even if it should be obvious that Herace is not his daughter either, she at least looks the part (the typically dominant blue eyes and black hair, though it's said there were exceptions to that rule in the past), came with the keepsakes of their mother, and he already seems to like her, while Bebe is the stone that rolled in from who-knows-where, without any (publically known) reasons.
Though I just read chapter 41 and it made my theory of her being just a mother for show pretty solid. Like, I knew she was probably really the Duke's child, but that would literally mean her "mother" can't be her mother, so I was wondering if it was too far-fetched. But everything from her moment of waking made it clear - the late emperor treasured Bebe, yet not a soul knew about her, not even a priest was called in, even though it's apparently common practice. If you had kidnapped a child, you wouldn't even want your fucking priest to know, amirite?
Anyway, the moment she told her, her real name was "Beatrice" or nicknamed "Betty", but she wanted her to be "her" Bebe, it was clear this isn't her child, she simply wanted her to be. I don't doubt she feels real feelings as her mother, she even gave her life trying to protect Bebe, but this bitch knows who's child "Beatrice" really is. Like, she made it too obvious that she knows.
How the other sister and brother saw proof that’s they real sister and still acting the fool? He literally said “she looks just like mom when she was younger “ BRO IF 2+ 2 =4?? Ykw it’s the dad fault, he did NOT raise them correct w common sense