The C is important because it's a family name. We would call her Cate. My only hesitation about going with Catherine is that it is rhyme-y with Addison (DD) and doesn't fit as a sibset in terms of style. My hesitation with Cate is that it is a nickname & doesn't give her as many options.
Married 12/8/07 | Sleeve Gastrectomy 10/19/09
BFP#1 DD born 3/9/11 | BFP#4 DD born 9/20/13
BFP#2 6/21/12, M/C at 5w2d | BFP#3 11/27/12, M/C at 6w6d