Darica felt very touched and emotional actually, as she listened to Duke's confession.
It wasn't easy for a man to admit openly his wrongdoings, especially to a woman. Knowing how Duke at times wanted to have control over the relationship. And now, seeing him humbling himself like that, she finally began to see that Duke might love her.
And that realization was enough for her to soften her expression, which had turned a bit cold when she was listening to Duke speaking earlier.
Seeing that Darica was accepting his confession and apology, Duke felt that his impromptu decision to confess was indeed the best.