Totally agree with @Andrea-and0 Francis . I too have a strict no pet policy (regardless of category) on one of my listings for the exact same reasons, my second listing it is pet friendly although all pets must be housed and contained on a secure patio not in the unit and must be control leashed when in the grounds of the property.
I own pets myself on this property and they are fully contained @ all times and leashed at any time I take them into the public areas.
If people dont agree to this then they dont stay.
I would be devestated if I had to put one of my family members to sleep and that is what my fur babies are.
My heart goes out to you @Lee-Marie0