Do you have a contract?
If not... there's no time like the present!

If you do, here's a good thing to add to your sick policy:

Outline symptoms that would require the parent to come and pick up. Require in writing that it is the parent's responsibility to have alternate care for the days that their child is sick. Have a space allotted for that name and number.

Then if the parent can't miss work, you have another number to call. If the alternate care provider won't/can't, it's ultimately the parents responsibility!