I would call your licensing and ask what you need to do in order to administer a nebulizer treatment. (I had this as a child because I was born with asthma. Also had to take it during elementary school in the nurse's office too.) If it is considered medication, does your handbook have anything about you NOT giving any forms of medications? Mine does with a parent consent and they must fill out a form. If you don't though, I would ask if you are required to give the treatment when you call.
If you just had everyone turn in a new contract today, I wouldn't want to have them sign another one. Did you raise your rates too? If you are going to term down the road, I would wait a bit as you are advertising and let others know you might have a spot opening soon.
Then, term once you have documentation of one more late pickup or early drop off or late payment. You obviously have records of these from the past, if not, create them.
I wish you the best of luck. You should also ask the mom for the dr's name and number because you "have a few questions to ask him" that you will not share with the mom because.....you will call and mention you are the child's provider and want to know if they really get reimbursed for daycare costs and when or whatever other questions you may have.
Also, if you honestly feel you cannot provide the proper care this child now requires, that is okay to term with that being said and a two week notice. I read it somewhere and it is NOT discrimination. It's honesty and caring and if you're unable to provide the proper care for this child's newly aquired needs then it is best to let them know. You could even try it for a week or two and then decide.