No pets are permitted on the premise without prior written consent of the Landlord.

That once you begin painting and working outside the pets will need to be contained in the house during the work.

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.

I even eliminated pet fees unless you have more than 2 (i usually turn more than 2 pets down anyway). 

So, security deposit and pets deposit can be apply towards it. 

The problem deepens: The old landlord chose to go with a non-standard lease agreement that does not cover the topic either smokers or pets in any way, not even a passing mention (and there's no addendum for either as well).I want the two male tenants out; I have been told that they are smoking in the house (including marijuana), though at the moment I do not have any personal verification of this (I do know they smoke outside). 

I would like them to vacate for many reasons, most importantly is that they are hoarders, have cats with no pet addendum or deposit and have let their side of the duplex fall to disrepair.

Keeps pet odor (the ones they say they never have) easy to maintain.

Perhaps the issue here has to do with your pet policy.

NEVER NEVER NEVER USE A THIRD PART SERVICER TO COLLECT SECURITY DEPOSIT AND 1ST MONTHS RENT BEFORE MOVE IN.I always use Cashiers check or money order for the security deposit,pet deposit and 1st months rent NO EXCUSE,Period.If tenant cannot do that well i am moving away.Until the security deposit clears in my bank account i donot hand over the keys how frustrated the tenant is.Another key thing ,the more pushy the tenant is in getting the place the more shady the tenant is and i will always double think @ that point.