I had a small commercial (£50 a month) try this exact same idiotic thing.
They had this rubbish, but large, window cleaning compnay that used mainly polish workers who could hardly speak any english, looke scruffy, were rude etc. They kept missing windows, tramping mud inside the buidling (a little bit of insides are done too), never turning up when arranged etc etc.
So when I started, they were overjoyed. I never miss windows ever. I am fastidious about turning up exactly when I say I will, I always use shoe covers when going inside, and I have a coroporate branded polo top so I look professional etc etc.
Anyways, after a few months with no problems, the woman called me and said the old window cleaning company had called and wanted to come again, so now she wanted me to do alternate months with them.
I said "I though you weren't happy with them, hence you hired me?"
"Oh well I don't like to say no, they've been coming such a long time" It was 2 years.
I was pretty annoyed by this, as all she had done was complain about the old lot since I started.
I put her straight. I said "look, I don't do time share. Either you want me to come, and you have seen how I do a good job and am reliable, or you want them. It's your choice"
Well she didn't like that. She got an attack of "I'm the customer and always right" and said she would think about it and get back to me. Fine, I thought, she had already entered the dropzone as far as I was concerned for suggesting such an idiotic thing. I don't do them.
A few months pass, and she gets her husband to call (CHICKEN!) to ask me to call regularly every month again as before. I say "So it didn't work out with your other guys then?"
He says "erm, yes, well, perhpas it was a mistake not to just let you do them"
So I say, ok I'll resume, but no more messing about or that really will be it.
So next time I turn up, start cleaning, and hear a bit of a rumpus inside, some shouting going on. Bit strange. Try to overhear, and catch a few words here and there, and realise they are arguing about me. So I just continue.
I go inside to give them the invoice, and the woman is there with the man looking at her sternly. He says to me, "thanks, a great job as always, WASN'T IT MARY?" at her.
So she said, almost through gritted teeth "Yes, and I wish to apologise for messing you around and it won't happen again"
I make light of it, to try to reduce the tension, and all is well.
Three months later, and everything seems to be fine still.
The moral of the story is don't tolerate idiotic suggestions by customers.