Lady Croom may disapprove of "women [...] got up like jockeys" (2.6), but she definitely wears the pants in the Coverly family. Watch as she commands the lesser mortals who surround her at Sidley Park:
LADY CROOM: Thomasina, you had better remain. Your knowledge of the picturesque obviously exceeds anything the rest of us can offer. Mr. Hodge, ignorance should be like an empty vessel waiting to be filled at the well of truth – not a cabinet of vulgar curios. Mr. Noakes – now at last it is your turn – (1.1)
Lady Croom doesn't even allow the others a chance to answer – that's how secure she is in her sense of her own power and superiority. She speaks in direct statements and commands, with no room for disagreement. When other characters do behave in a way she doesn't like (Mrs. Chater and Lord Byron, we're looking at you), her justice is swift, and "banishment" (2.6) from Sidley Park is the penalty. Setting Lady Croom up as the tyrant of Sidley Park reinforces the idea of the estate as its own little world, the universe in miniature.
If Lady Croom is a tyrant, she is mostly a wise one. Sure, Septimus is flattering her when he says "Your ladyship should have lived in the Athens of Pericles! The philosophers would have fought the sculptors for your idle hour!" (2.6). But we get enough of her wit to suspect there's real admiration under his compliment. Thomasina shares Lady Croom's intelligence. This suggests that, if Thomasina had lived, she might also have shared her mother's fate: queen over a small kingdom, leading a domestic rather than a scientific life.