Margaret More (Susannah York) is More's whipsmart daughter. She's very much her father's child—she's incredibly intelligent and even knows how to speak better Latin than the king (as is made cringe-worthily clear when Henry visits Thomas More's house). She may want to marry a Protestant, Will Roper, but that works out when Will decides to switch allegiances for love—a nice gesture, though not one More himself probably would've made.
Ironically, Margaret and More's loving wife, Alice, tempt him to relent far more than Cromwell ever could. After More is imprisoned, Margaret tells him,
MARGARET: We don't read because we've no candles. We don't talk because we wonder what they're doing to you.
MORE: The King is more merciful than you. He doesn't use the rack.
Bending Principles for Love
She also tries to convince him through argument, but that doesn't fly either:
MARGARET: Father. "God more regards the thoughts of the heart than the words of the mouth." Well, so you've always told me.
MARGARET: Then say the words of the oath, and in your heart think otherwise.
MORE: What is an oath then but words we say to God?
More goes on to explain that he would be sacrificing his own soul and principles by swearing falsely to the oath—to Margaret's disappointment. Ultimately, he entrusts his family's fate to God, and accepts death. Interestingly, Margaret doesn't seem to be lacking in principle herself—she just doesn't want her Daddy dearest to die. Who knows what might've happened if she and More had switched places? Maybe he would've been trying to get her to take the oath to save her life… and she might've been resisting.
According to the movie's epilogue, after More's martyrdom, Margaret actually took his head down from Traitor's Gate and kept it until her death: faithful (and really, really creepy) to the last.