Get the herd to change behavior. 

I could not disagree more with your 3rd point - why on earth would you want to reward bad behavior with a 3-month free rent gift?  

So if it were me, I would give the tenants the benefit of the doubt.I am a car salesman by trade and student of human behavior and it sounds like these tenants have the same problem that many children do when they are not met with firm boundaries: They are doing whatever they want.As the new owner, you have the fantastic opportunity to lay down the law in a way that the current owner (who sounds like a terrible businessman) really can't (not that he would anyway).Just like a new babysitter has an opportunity to lay down the ground rules with kids who were previously unruly, you can sit down with each tenant with a properly drafted lease and have a very serious discussion.

This behavior has been preventing me from securing a new tenant.A lawyer is held to a higher standard of behavior with regard to interfering with a person's ability to conduct business. 

She is just so adorable that we let her get away with many behaviors like barking at us and lately even growling.

Perhaps with a better understanding of how to make clear protocols and what will be accepted behavior up front would make this easier.

If you show weakness and back down to the tenant's threats, they will walk all over you - and it may also be used in court to show you allowed the behavior, so now you can't complain about it.

Most professional landlords and property managers don't play the cash for keys game and that is for a good reason.I also agree with Mindy that rewarding bad behavior is a not a good idea.

If you have bad tenants, who from the beginning, sought to over-pack a Rental, with many people living in it; then their behavior will never end, including with who were invited in, to over-crown the Rental.

I dunno...all I can say is that maybe being forced into being irrational breeds more irrational behavior.