You can report vandalism, vacant properties, drug dealing, potholes, broken streetlights, derelict vehicles, nuisance properties, loose animals, overflow of trash, etc.

Only after the tenant fled the state was it discovered the extent of trapped animal damage (horrific to say the least). 

Animals outside your property is not your responiblity but if they are nesting under your house then you should take care of it Make sure that the tenants are not leaving out cat food and are securing their trash.

They might be breeders, or they might be animal hoarders, or they might be crazy... any way you look at it, it's an absolute NO to me. 

I want to make this smoother for both of us. 

In an attempt to offset the risk/damage that I believe the pets will cause, on average, over time, I charge the following per animal:Cats: $200 move-in fee, plus $25 per monthDogs: $200 move-in fee, plus:- $25 per month for a small dog (less than 25 lbs) - $50 per month for a medium dog (25-50 lbs) - $75 per month for a large dog (50+ lbs) Additionally, I must meet the animal, and preferably at their current residence, prior to move-in.

If a tenant has an emotional support animal or service animal, none of the "pet" language applies, though.You should create an Animal Addendum, or Animal Clause, that applies to all animals, whether they are pets or not. 

The more you explain upfront, the smoother things will go.

If you do allow it, just be sure to explicitly state on the lease and explain verbally that they are allowed "2 Guinea Pigs" only and that any other animals are prohibited without your prior written consent.

call animal control.