Letter to end lease?

[Katie Stone]

We have had a tenant that has been living in our duplex for about 2 years.  After year one  the contract goes month to month.  We no longer want them to live there.  We found out today they have a dog (we have a strict no pet policy- and when they asked 6 months ago we said absolutely not).  We are worried that they will damage the apartment (the husband has had a restraining order in the past from the wife, but moved back in without us knowing as well).  Yeah, we picked a winner (we actually thought they were great at first, with no criminal records, and fit our strict criteria).  Anyway, what is the best way to get rid of them nicely, but firmly?  She also claimed to the neighbor that the dog is an "emotional support animal".  I don't want to get into any legal problems. Help!