I disagreed with Peter's interpretation of that moment. I believed that Clarissa said "my" as an indication of possession. At the moment just before Elizabeth breezes in, Peter is in the midst of interrogating Clarissa about her happiness - if she is truly happy with Richard, which I believe (hope) was in a mostly platonic fashion. Although Clarissa was fantasizing about what life might have been like if she had married adventurous Peter instead of conservative Richard, her loyalty still lies with her real husband. So when she is caught in a slightly compromising position (Peter is holding her shoulders) by her daughter, she introduces Elizabeth with a "my" in an effort to make a distinction about where her place in this world lies, about where she is supposedly happy.
Or perhaps Peter's interpretation concerning the seeming existence of nonexistent bonds is not far off the mark. I read that the 'strong bond' was to be shown between Clarissa and Elizabeth. But perhaps Peter was referring to the bond between Clarissa and Richard, and simply used Elizabeth as an intermediary as she is their daughter.
I think there are many ways to interpret this scene. Thoughts?