Hi C.,
I have a child with autism who also takes every little cold virus hard. The reason that these things hold on for her is that she gets secondary infections that are very dangerous for her, but not contagious for the other people that are around her. A virus lives for several days and runs it's course, and secondary bactieral infections are usually not a threat to others.
Just my two cents, but we have a good relationship with our school nurse, and when my daughter sounds horrible, but is otherwise well enough to attend school, they let it go. If she is too sick to be at school, that is difffent, and we keep her home. We consut with our doctor about what is contagious and what is not, and if you had this kind of relationship with the Mom of the Downs child, could you stand to be around a child with a lingering illness that is not a danger to anyone else? I would make sure that you are not cutting her off for the wrong reason. It is quiet possilbe that the child is not a threat to others, but is only a burden on you to care for with snot and coughing, and to be fair to the Mom and child with Downs, I would find out if she really poses the threat to others that you seem to see here.
Certainly, kids who are contagious should not be with other kids, but once you know the facts, beyond that, what can you tolerate? I know that my child may get a simple cold and then cough for three weeks. She has few social skills, so it sounds horrible when she coughs and she does not try to sheild you from that and she is sure not bothered by her own snot being there for everyone to see. A child with Downs is going to be the same way. Are you sure that this is just not a euphamistic way to say that you can't handle the task? I know it is gross, but that is how it is with kids who have developmental issues, and it takes a special person to deal with it. Just saying, you should call it what it is, there is nothing wrong with you if you don't want to deal with that. You get a choice (some of us don't) but you do. Are you up to it? If not, just say so.
M.