@Pen3 I don't think she cares for him one bit, I just think she views him in terms of a sunk cost fallacy; since he was the heir to the family titles, they probably spent a lot of time, effort, and money on his upbringing to ensure he would be a proper Duke when he inherited the title, so writing him off would waste all of that. Walter, aside from growing up knowing that he was the spare, probably also didn't have those advantages, so they don't want to make him the heir, because they then get, in their eyes, a subpar heir to the family titles. The mother is probably also one of those who believes that the nobility shouldn't even know the
names of commoners, much less fall in love with one, which is why she's so against the Duke being together with Alice.
All that's just a guess, though, since we haven't really seen enough of her to really get a good feel of her personality, but it's what makes sense to me from what we
have seen.