Outrage is probably too strong an emotion. Try being a little angry instead. You'll find that it feels much better. Once you've got used to that, try turning it to slightly annoyed.
Resigned to the odd ways of other people is an even better emotion - and is easily within your reach should you choose.
Instead of an angry letter, why not something like:
**********************************
Dear Customer,
I'd like to thank you for your custom over the last few months. I quite understand that you wish to return to your previous window cleaner. He is very lucky to have such a faithful customer as you.
With my very best wishes
A W Cleaner
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Just think what a wonderful testament that letter is if she shows it to her friends and neighbours.
Love your site Wally! I think your letter is good (fiery coals and all that) but how about this:-
Dear Mrs Customer,
I was saddened to hear I was losing you as a valued customer; when we started I did make it clear that I was only able to take on customers on a permanent basis and your returning to your previous cleaner after his long absence has meant other potential customers have been turned away.
However I do understand you feeling awkward about your previous cleaner turning up unannounced and please be assured I have no hard feelings about it. If he should disappear once more I would be happy to take you back onto my books but have to stress this could only be on an ongoing basis. If he should turn up again I would hope that your loyalty would remain with me this time.
Much love and best wishes 
Laydown and Dye Window cleaning ...
These letters would be a waste of time...
You're assuming she can grasp the concept of sarcasm, when she obviously doesn't understand the concept of loyalty!
There was no sarcasm intended.
Why be sarcastic? It just makes me look small and gives other people something to either detest or laugh at.
Being tolerant and understanding of other people's funny little ways will take you much further and you'll enjoy the journey more.
And as Mr D pointed out. These customers pay our wages. They all have friends and neighbours and frequently talk about us. What do you want them to say about you?
Oh, yes. He wrote me a snotty letter. Here have a look at this
or
And he wrote me a very pleasant little note. Here have a look at this.
Which one says about you the things that you want people to say?
Which one is likely to get you more and better-quality customers in the future?