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.

If it’s really bad pet odor you gotta pull the carpet and toss the urine soaked padding out

I don’t mind keeping the tenants but I know the lease agreement may be to relaxed in areas such as smoking in home which is a No No for me and my properties so certain things I want to change but I have no problems at this time with keeping the current tenants other then smoking and certain things like pet requirements.

I have a checklist I walk down each visit to look at plumbing, locks, smoke detectors, windows, pests/mold, overall condition, pets, etc.Scheduling them is the biggest pain.  

I am pushing 2br 1bath units to $750.00 for about 900sf, plus $25.00 pet rent, per pet, two pets max.Those are on 8 apartment complexes total. 

I don't think you could find many people here who would/could pay a huge security deposit unless it was a special situation like a large # of pets owned.