I wouldn't think a doctor would tell someone the child "has" to have a puppy, or that it "has" to be a puppy and not a dog. If you allow the pets though, it seems you have to allow this. But I am sure the lease states the fees, etc. and they need to pay them and what not. Maybe suggest taking the puppy to behavior classes or something. Maybe you can use part of the monthly fee for the dog to help cover the classes for the puppy.