It's up to me to set the boundary about what I will listen to. If you don't want to be involved in the goings on of someone else's drama, it's as simple as saying "I'd rather not hear about that." If the gossip begins- I end the conversation and may not trust that person unless they prove to me that they have my best interest in mind and will respect my feelings and wishes.
Your cousin is being successfully used to get to you, what you decide to do about that is up to you.