I am a childcare provider would not allow a child to come to my facility and risk the other children getting sick, try and put yourself in their shoes I don't think you would be happy if another mother brough their child to a childcare facility sick and got your child sick, I know I wouldn't. Yes, I know it put you in a burden w/work but that is the price we have to pay as a mother and father. I know a lot of parents switch off who takes care of the child while the other works while the child is sick.
I am a single mother and thank god I have my parents help and support and I know if for some reason my parents can't take care of the baby and if all else fails I would go to my ex and his parents or a friend.
I know once I finish school and start working out of the home that is something that I will have to bring up to my employer before hand, that is one of the main reasons I decided to stay home w/my son and take care a few children from my home because my son was getting very sick at the day cares and in home daycare every time i turned around and being a single mom I couldn't risk missing all the time and paying dr bills and prescriptions.
I really don't think there is a childcare out there that accept sick children especially w/a fever and they have to be fever free for at least 48 hrs as well as if the children is miserable and seems to be sick the facility will call the parent to pick them up and will require a dr's note. I know this because I have worked at several day care facilities through my years.
Good Luck!