DLD all opinions are important and should be considered by everyone participating on this forum so I hope no one "jumps" on you for expressing yours
My view on this is that while these parents seem wonderful, they failed to read the important information package you gave them upon enrollment. I find this really disturbing as wouldn't you read this as it was given to you by the person who will care for your child??? They have breached a couple of your policies already. Doesn't bode well to me. So under the umbrella of "respecting" you, they are now trying to change the way you operate. It is not your responsiblity that he kept the child home and paid for a nanny. That was his decision, not yours, and he must bear the responsibility of having to double pay for child care. He came looking for alternate care and needs to abide by the policies. Did he short change the nanny because he was also supposed to pay you? Don't think so. I know how tough it is to get clients, I haven't been full myself for a long time, however I would stand firm regarding them paying for sick days. I have a parent wanted a monetary favour and I just stated I wouldn't do it as it wouldn't be fair to my other clients who pay the full fee.
So my opinion is stick to your policy, no rewards for not reading the paperwork. I hope it works out for you whatever you decide after all it is your daycare/your rules