I was really interested to read your question, because from the title, it seems as though I have the same problem as you with one of my oldest friends. As I read more, I realized that I would probably be your cousin in this relationship (but not as extreme). Let me explain.
I love my kids. I love spending time with my kids. But I am not an attachment parent-er. We Ferberized my daughter at 18 months. I do like to get a babysitter and go out with my husband (we try to do this once a month). If my 5 year old daughter falls down, instead of running over, I'll often just say "you're okay. Try getting up and walking around." I encourage my kids to eat fruits and vegetables, but at the end of a long week, they have mac and cheese for a couple of meals in a row, that's okay.
My oldest friend, however, hardly goes anywhere without her daughter. She buys only natures miracle diapers. She nursed her daughter until she was 2.5. She coslept for 2 years. You get the picture.
Anyway, I often feel judged by my friend. It is very very hard to be friends with someone who acts like they love their kid more than you love yours. She doesn't seem to acknowledge that I have two kids while she has one, or that she has way more financial help from her family than we have from ours. Because of both of those things, sometimes I have to make choices that she doesn't make. And we have different priorities - I never wanted to cosleep, for example. It doesn't mean that I don't love my daughter as much as she loves hers - love manifests in different ways.
So my advice is twofold - if you think that your cousin is really disturbed, then encourage her to seek help, especially if you think that her behavior is dangerous to her kids. If you just think she's not a good mom based on your idea of what a good mom does, either stop being friends with her or try very hard not to judge her choices.