More fuel for the fire, a first draft, suggestions welcome. And thanks to all who have already provided me with support and excellent feedback, I feel less like I am going insane.

Yes I would prefer to be doing other things, but I think it unfortunately needs to be said if I am going to continue with them:
(name of parent),
Unfortunately, unless you have a specific question regarding what I am teaching, or what (name of student) is to be doing, I’m afraid that I simply don’t have time to become involved in melodramas of this kind.
Where you stand financially has nothing to do with me at this point, but I do encourage you to familiarize yourself with my policy, which you should already have done before we began. I have no information that you don’t.
Furthermore, since I have consistently taught 30 min longer for almost every lesson, which I keep a record of after each lesson, I believe those extra hours means I am currently working at a loss. This would also include the time I spend outside of lesson which is normally at least 2 hours per week per student.
It is your responsibility to ensure (student) comes to lesson prepared, and prepared to learn, not to have a party with her friend. No amount of structuring the lesson is going to help unless that is taken care of.
You have not done what I have asked, which was to download the lyrics for about three songs which the girls were to work on learning before you went away on your trip. And the girls failed to do that again since our previous lesson. This is not a problem for me, but if it is for you, then please do what I have assigned.
As chance would have it, my voice memos recorded the entire lesson last Tues and I can show you numerous examples of learning. I’m not sure how you are defining learning, it's a little vague the way you say it, but in my experience the real bulk of learning takes place outside of lesson, during her own daily practice, which at the moment appears to be not happening. Again, this is your responsibility to ensure it is happening, and so to accuse me of not 'teaching' her anything I find to be just a bit offensive.
What I do is show students how to practice, but the students are the ones who do the work. You have got it backwards, what she learns comes from her, not me. I have nothing to teach. This is an unfoldment, and it happens in ways that look very much like this.
Finally, please be aware that lessons are given freely, and as a community service to expat and local families who I choose to work with here in (name of city). What I charge is to allow this service to continue. If you don’t feel this service is of benefit, then I would kindly ask you to allow another family to have the time I have set aside for (student).
Thanks!