I work on the principle that, if I am available to work the contracted hours, the parents pay for the service and, if I'm not available, I do not charge.
It has always been seen as fair and reasonable by parents and everyone always knew where they stood.
I certainly wouldn't agree not to charge for a child who was ill because I would still be available to work.
If I am unable to work through my own illness, my children being ill or for any other reason, the parents have to pay a different childcarer so it would not be appropriate for me to charge them.
To expect your childminder to make no charge, both when she is unable to work and when your DS is ill, seems unreasonable as she takes the hit both times.
Unless she charged you when she couldn't work due to her own child's illness (which isn't clear from your posts), it is not reasonable to expect her to lose out financially due to your child's illness.