Newer block homes 1-1.5 miles outside of the central town still do well also, especially if kid and pet friendly. 

We have two dogs a pit bull and a chiweenie, but as a landlord we will have a no pet policy.

If you were a renter that didn't want to ever have to worry about a barking dog, had pet allergies, or had emotional trauma from bad experiences in the past with pets (especially dogs), wouldn't you be happiest in a no-pets unit, on a no-pets rental property?

Next we find out that she has 2 kittens in the house even though the lease specifies no pets. 

Pets?

Management company wants to keep pet fee, I want to claim the pet fee and be responsible for any damage.

We are priced about the same as the apartments, and while we don't have a gym or pool, we do have a yard and accept pets. 

We’ve had an apartment sit vacant since August and have had no luck finding decent enough tenants that don’t smoke or have pets, have no felonies and no prior evictions.

I guess I could call one of their past landlords and see what damage his pets did to the house and see if they have any ideas.

Check the furnace filter, make sure downspouts are attached/down, ensure tenant is caring for landscaping, check on smoke detectors, are there evidence of pests, does it look like more people are living here then indicated on your lease, and finally is there evidence of pets not on the lease.