At times, Thomas More acts way more affectionate with his daughter Margaret than with his wife Alice. There's a good reason for this, however. While Alice has what More doesn't have—namely, boldness and brashness—More sees his spitting image reflected back at him in his daughter's eyes.
After all, Margaret's the only character in the play who can be counted as More's intellectual equal. We see this in her Latin conversation with King Henry VIII, during which she proves herself to have a superior knowledge of the language—a knowledge she credits to "the skill of the master" who taught her—none other than Sir Thomas More (1.515). But we also see it in More's frequent asides to Margaret, as they show that he's trying to impart his wisdom to her more than to anyone else.
This is a sharp contrast from More's relationship with his wife, Alice. More admires Alice because she's so unlike him: she's brave and bold in all of the ways that he's not. In Margaret, however, he sees someone who shares his same bitingly logical mind, as well as his unquenchable thirst for more knowledge. And that's a rare thing, if you ask us.
Interestingly, the fictional Margaret More is pretty similar to the one we find in the historical account. Margaret More/Roper was one of the most highly educated women of her time, a successful writer, and the primary baton-carrier for her father's legacy. It may give us some comfort knowing that Thomas More's brilliant mind lived on past his death. Hopefully not literally, though. We don't want another Frankenstein situation on our hands.