He just asked for a therapy dog and I said sorry, still no pets.

Some judges are pretty lenient except for non-payment of rent...so if you are trying to evict for lease violations that may not happen...one too many cars, pets, extra people, etc.Also make sure your eviction letter is not pay or quit....it's just quit....as some judges will interept pay or quit as that....if tenant pays...well that is what you asked them to do.I would also see if there are a bunch of attorneys hanging around trying to pick up tenant clients. 

Asked her next door wich is my another tenant and she hasn't hear them or thier pet sounds.

This gives you a comparison to the level of mold spores that are naturally occurring and are "tracked into" the house on people's clothing, pets, etc.

Quick note - regardless of term if you allow dogs or the tenant has one undisclosed and the dog bites someone or another person's pet the attorneys for the injured party will name the dog owner to the suit (obviously) but also name the homeowner to the lawsuit even if the event occurred off site such as walking the dog.You can say that's wrong all you want and I'd 100% agree - this is how it works.Your first layer of protection here is the tenant having renters insurance (that does not have an exclusion for dog bite or an exclusion for the tenant's dog breed).

Think of all the things that could go wrong and see if the lease addresses them: unauthorized pets or tenants, early termination, security deposit, lease violations, late rent, eviction, lawn maintenance, parking, etc.5.

One final thought is whatever you end up doing, allow pets.

On top of that they encouraged me to allow pets and rented to someone with cat and dog and they told me they keep the pet rent.

Keeping track of sets of keys everywhere is one of my pet peeves. 

(can you tell it's a pet peeve.)