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.

I put meters in and it changed their behavior. 

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."

I determined the property characteristics that attract the segment with the behaviors necessary for a reliable income.

The neighbor who is living there has developed a pretty bad mental health issue and has become very erratic and displaying violent behavior even threatening to kill me and my tenant.

Never EVER accept or agree to accept any tenant without properly conducting all points of discovery and creditworthiness [ability to pay], background [character] data [patterns of behavior in past residences], etc.

I suspect that is driving some of the behavior you are observing.  

Usually when there's behavior like this, from VRBO or other companies, there's a stretch and they have already knocked on the door of consolidation via acquisition(say booking or airbnb).

Issue a Written Notice: If the behavior continues, issue a written notice citing the lease violations.