Anonymous wrote:You have a no pets policy right? That right there should be a good enough reason.
I would worry that the cousin would try to dump her pets and still get the house, in that case. Don't leave loopholes open; don't put the pets in jeopardy, at the same time. (Also, please consider people with pets - we are so grateful when landlords open their homes, and will by and large pay enormous deposits to cover any extra wear and tear.)
I don't know what you can say here that's going to eliminate drama - seems like the drama is baked into the whole situation. I think you just need to deal with your cousin being pissed and perhaps even some people taking her side. That does not mean you should rent to her.