The best evidence is a video recording of the alleged conduct.The "problem tenant" allegedly "telling them what to do" doesn't appear to be behavior you can prohibit, unless it rises to the level of disturbing the peace in violation of state or local law.

out our way these letters are usually far more than letters they can be a bound booklet.. with pictures of the family  the family dog  the family parrott  pics of their kids at the beach etc etc.. long flowing letters. 

Never one to kick a down dog, but for future investments, I would strongly advise against ever owning an investment property in an HOA neighborhood, especially an STR.

I put meters in and it changed their behavior. 

If there's one thing STR investors welcome in the PNW... it's dogs with three of the top 10 locations for pet friendly AirBnB's located in Oregon & Washington. 

If they refuse to move out, evict through an attorney.When I tell tenants to leave because of lease violations or criminal behavior, they read the writing on the wall and move out 80% of the time. 19% will stay the full 30 days, or close to it, and then move out.

Tenant therefore agrees (a) torefrain from any behavior which is loud, obstructive, rude, offensive, boisterous, or disorderly; Any violation of this paragraph may, in Landlord’s sole discretion, be cause for termination of the Lease and or Tenant’s tenancy."

When I rehabbed the basement I tore out the existing drywall ceiling and added sound-proofing insulation followed by a 5/8" fire-rated drywall thinking that would be enough, but apparently the tenants can hear us walking, the dogs claws (we have hardwoods) as well as the TV.

What type of dog is it?

I can do a wet paper towel test afterwards and it comes up pristine, but I also have a dog so it doesn't last long :/