Hi, A..
I have a 2 1/2 year old son who goes to daycare twice a week because I work full-time. (My mom watches him the other 3 days) I, too, have the frustration of seeing many of the kids at the daycare with green runny noses, coughs and red-rimmed eyes. Some days that I pick up my son he's even got the little crusty nose if they've been outside and no one has cleaned him up. VERY FRUSTRATING!! My son stays home when he's sick but I also have the option of keeping him home due to a very understanding boss and the help of my mother. Some employers aren't as understanding when parents have sick children - so the parents are almost FORCED to take their sick kids to daycare/school for fear of the boss' reprimand or even losing their jobs.
I believe cleanliness on the part of your daycare provider may be part of the issue and is SO important. Children will wipe their noses with their hands, cough without covering their mouths and put their hands and other toys into their mouths. ANY environment with children will be this way. Some illnesses will spread with such close contact and is almost unavoidable, even in the cleanest of environments.
I had an in-home daycare a few years back and was pretty successful keeping illnesses from spreading with EVERDAY cleaning and disinfecting of all the areas the children were in, cleaning and disinfecting ALL of the toys, using all white linens, blankets, (each child having their own diaper changing linens etc.) for easy bleaching and handwashing VERY frequently using disposable towels. AND, keeping runny noses wiped so the children didn't wipe with their hands and spread germs. It's ALOT of work and I fear some providers aren't as diligent as others in keeping up with the cleaning throughout the day and after the children go home.
Illnesses are part of life and do build immunity but that doesn't negate the importance of trying to prevent these illnesses in our precious little ones. You may want to sit at daycare with her for awhile one day and see how she handles cleanliness issues. That may help with your decision.
Sorry this is so long. Hope it helps a little. Good luck!
J.