I agree with mumofsixbirds. If a person's well-being is concerned, it's a completely different thing from non-essential 'treatments'. The pissed off moo is a complete ass in the medical situation and should be charged with child endangerment if she wants to prevent the child from getting medical care. But about the eyebrow...
What if the kid had sensitive skin and got a rash because of it? What if the parent is concerned about imposing beauty standards at a young age, and wants the kid to just be a kid? What if the parent just didn't think of it and is happy with the outcome? What all these scenarios have in common is that in none of them is the daycare worker justified in performing the unsolicited waxing.
Just imagine how pissed off you'd be, if you went to the dentist, and while you were having your teeth examined, a hygienist decided you'd look better with a different hairstyle...and proceeded to give you one. It is largely irrelevant whether the end result is good, such extreme presumption is completely unprofessional.