According to the Oxford Dictionary of First Names (c1996, Patrick Hanks and Flavia Hodges), Karen is the Danish form of Katherine, and since Katie is a common pet form of Katherine, I assume that's why Karen uses it. Like ankaret, I think Karen must have used Katie when she went to university, and Edwin calls her that because that's how she was introduced to him, or else how she introduced herself.

Maybe Edwin objects to relative strangers nicknaming his children? I have a name which is commonly abbreviated to short forms that I dislike very much, and I have met people who instantly use those short forms when I've introduced myself using the full form of my name. I also regard Fob, at least, as more of a nickname, than a pet or short form. And it may be that he sees Fob as a ugly nickname for a name he likes very much.