You are the business owner so you get to decide if you will or won't take a child. It doesn't matter what the Dr says.
The Dr isn't assuming liability nor is the Dr allowing this child to come into HIS/HER home. Because it is YOUR home and YOUR business you get the ultimate say.
I understand this is a difficult situation but honestly it's a difficult situation for the family not you.
They need to figure out how to manage their child's illness, disease and/or condition and not expect others to figure it out for them.
It is NOT discrimination to exclude him or refuse to enroll in your program. You can not get in trouble for saying no.
As for managing in the classrooms..... again it's the family's issue to figure out. Each place more than likely has a rule to protect the health and well being of ALL kids enrolled so more than likely the preschool would have a rule of all spots being covered with long sleeves and/or Band-aides. If child has trouble following those guidelines or keeping Band-aides on, he may very well be excluded from the preschool classroom as well.
Here is the info sheet my state provides for this condition. It explains how it's spread, what you can do to prevent and/or treat. I am not providing this so you re-think taking this child...I am only posting the link as informational. Whatever choice you make (enroll or exclude) is 100% YOUR choice and neither choice is wrong.
http://www.hennepin.us/-/media/henne...ider.pdf?la=en