I think people don't really know how to react to a D. So when someone tells them they have filed or are getting a D, they sort of want to not be involved in it cause they're not sure waht reaction you want (agreeing with you and/or telling you you've made a mistake or being against or for the divorce). Like perhaps they're trying to gauge how you feel about the D so that they can later react to it. Does that make sense? Also people tend not to want to press further. BUT I agree with you---D is heart-wrenching and sometimes all you want to do is pour your heart out to someone.
If your cousin asks how you're doing you could tell her you filed and are feeling down and would like to talk sometime about it with her, etc. She may feel awkward and unsure of how to respond to you if you don't let her know that you're "not ok" and want to talk.