A related discussion,
child cough was started.
I agree that the ceiling fan definitely stirs up dust not to mention how utterly full of dust the fan blades themselves have on them.
Maybe year eight of your marriage will be the one in which you will finally be right. The fan probably has little to do with creating the cough or making it worse. Asthma often occurs in young children with a respiratory infection. However it is not absolute that if cough is the only symptom, that this is asthma. This is particularly true if the medication only works 1/3 of the time. Asthma should respond much better than this. I would discuss the diagnosis more with your daughter
Having the fan on high all the time could be drying out your daughter's throat. This is especially true if she tends to sleep with her mouth open a lot. If she has a cold, or is stuffed up, this is pretty likely. Has your daughter been to a pediatric pulmonologist? It doesn't sound like her meds are helping enough (with or without the fan) Try convincing your wife to sleep with the fann off for 3-4 nights. If it is too stuffy for her, she might want to sleep in another room for a few nights. Just get her to give it a try, and see if it helps. This could be a good reason for your daughter to move up to her own room. In any case, a humidifier might help.
It could also be blowing pollen, dust,etc around and insighting allegies to kick up. I cannot sleep with a fan on in my room unless it is an airpurifier type. Maybe you should try one of the Honeywells that has a fan but purifies the air. I think your wife should do as suggested and turn if off a few nights or sleep in another room. Maybe it is just too crowded in the bed and not enough O2 around you all.