Pet Addendum in New York (not NYC)

Hey!

I have a no pet policy for my units, but one of my tenants worked around this by making her cat an Emotional Support Animal. I am feeling cornered by this and don't think that I have many options. A highly experienced real estate mogul out of Virginia gave me the advice to charge an extra deposit to help cover some of the damages, even if it isn't totally legal... Not sure how I feel about this approach. Do I just have to accept it and get the tenant out of the house when the lease is up?

Another variable in this situation is that she actually has two cats, but only one is an ESA. I could offer her to bring the other cat as well and then be able to charge a pet fee and a deposit? 

I'd appreciate any guidance here!

Thanks,

Colin