Yikes, I am sorry you are dealing with that!! I am also one of those who can not handle puke!! I've dealt with a lot of crap in all my years in child and healthcare but puke is the worst!! I have vomited myself after cleaning it up!! lol

I have had a few kids spit up/puke at daycare and if I KNEW for sure the reason (crying too hard, gagged on food etc) I have allowed them stay but for the most part, puking at daycare is an instant reason to go home. I feel for this child because her behaviour sounds like it's a direct result from her parenting but cleaning up puke that many times in just the morning alone would not make me happy and I'd call for pick up. I'd also explain to them that it's just not feasible for me to have someone like their child in my daycare for sanitary reasons as well as the fact that I have to be able to be available for the others. Sounds like she may need another daycare or perhaps even a nanny?