I think your concern and caring for your cousin is a wonderful gift she is receiving from you. I hope this response helps.
Tokophobia, the fear of pregnancy and childbirth, is a fear woman may have. Here is some information from an article on some of the most common issues surrounding this fear. Here is another with more description and additional information about it.
The key here is to identify it as what it sounds like it is, tokophobia, and seek treatment from a mental health professional that has some experience. You may want to ask the OBGYN community who they refer to for this.
Wishing you patience and peace,
Proof Positive Blog @ PsychCentral