I agree that "family' is a very important to a lot of the characters in this book. Olivier is still wearing a ring with a family crest from a long gone old French estate. Kate has her own sadly reduced nuclear family as well as her extended French family. Bastien is devastated by the break up of his family. The Schell family who all seem to be at cross purposes most of the time but do really care for each other and know they need each other.
I admit to being frustrated with Kate's rather trying too hard to be part of the Schell family. But I can as well see that she is also just doing what they all expect of her and really wants to keep her job.
I can think of a couple of reasons for her ambivalence about connecting with her French family. Etienne had not treated her well and she had no idea how he would look at her now. Jacques and Solange were very good to her, but have left Paris and are leading a very different life and I think she was concerned that she might not find them the same and not know how to interact with them.