In that letter,  list the dates and times of problem behavior and in the letter state that these tenants are disturbing you and your wife's right to "quiet enjoyment" of your property.  

Let them know the sooner you show it the sooner they will not be disturbed again.

If you have a good one, then it should have something in there about not disturbing others, peaceful enjoyment of the building for all, etc.

The fact that you are prepared to "take a risk" is disturbing.

It's only harassment if done repeatedly and in a manner that's considered disturbing and/or threatening. 

As for my tenants,  I can screen a tenant in one minute over the phone and I'm completely upfront with what I expect from them... no parties, to pay their rent on time, to take care of my property and not to disturb other tenants.  

If the parent can't control the kid, to the point the kid could disturb other tenants, you can deny her based on that.Also a credit score that "should be above 600" is horrible.  

@Harlowe Thrombey that is just covered as part of a noise disturbance clause in most leases.

I'll spare the details of long emails and voice mails that they have sent threatening us with all sort of legal action, etc. if we do anything to work on the unit that disturbs their well-being, or do anything that seems retaliatory.

A better movie for this topic is "Pacific Heights", where Michael Keaton's character makes a rent pre-payment (and engages in some disturbing behavior as well).